Probabilistic decline curve analysis (PDCA) methods have been developed to quantify uncertainty in production forecasts and reserves estimates. However, the application of PDCA in shale gas reservoirs is relatively new. Limited work has been done on the performance of PDCA methods when the available production data are limited. In addition, PDCA methods have often been coupled with Arp's equations, which might not be the optimum decline curve analysis model (DCA) to use, as new DCA models for shale reservoirs have been developed. Also, decline curve methods are based on production data only and do not by themselves incorporate other types of information, such as volumetric data. My research objective was to integrate volumetric information with PDCA methods and DCA models to reliably quantify the uncertainty in production forecasts from hydraulically fractured horizontal shale gas wells, regardless of the stage of depletion. In this work, hindcasts of multiple DCA models coupled to different probabilistic methods were performed to determine the reliability of the probabilistic DCA methods. In a hindcast, only a portion of the historical data is matched; predictions are made for the remainder of the historical period and compared to the actual historical production. Most of the DCA models were well calibrated visually when used with an appropriate probabilistic method, regardless of the amount of production data available to match. Volumetric assessments, used as prior information, were incorporated to further enhance the calibration of production forecasts and reserves estimates when using the Markov Chain Monte Carlo (MCMC) as the PDCA method and the logistic growth DCA model. The proposed combination of the MCMC PDCA method, the logistic growth DCA model, and use of volumetric data provides an integrated procedure to reliably quantify the uncertainty in production forecasts and reserves estimates in shale gas reservoirs. Reliable quantification of uncertainty should yield more reliable expected values of reserves estimates, as well as more reliable assessment of upside and downside potential. This can be particularly valuable early in the development of a play, because decisions regarding continued development are based to a large degree on production forecasts and reserves estimates for early wells in the play. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148436

In this work, a probabilistic methodology for Decline Curve Analysis (DCA) in unconventional reservoirs is presented using a combination of Bayesian statistical methods and deterministic models. Accurate reserve estimation and uncertainty quantification are the primary objectives of this study. The Bayesian inferencing techniques described in this work utilizes three sampling mechanisms, namely the Gibbs Sampling (implemented in OpenBUGS), the Metropolis Algorithm, and Approximate Bayesian Computation (ABC) to sample parameter values from their posterior distributions. These different sampling mechanisms are applied in conjunction with DCA models like Arps, Power Law Exponential (PLE), Stretched Exponential Production Decline (SEPD), Duong and Logistic Growth Analysis (LGA) to estimate prediction intervals. Production is forecasted, and uncertainty bounds are established using these prediction intervals. A complete workflow and the summary steps for each of the sampling techniques are provided to permit readers to replicate results. To examine the reliability, the methodology was tested over 74 oil and gas wells located in the three main sub plays of the Permian Basin, namely, the Delaware play, the Central Basin Platform, and the Midland play. Results show that the examined DCA-Bayesian models are successful in providing a high coverage rate, low production prediction errors and narrow uncertainty bounds for the production history data sets. The methodology was also successfully applied to unconventional reservoirs with as low as 6 months of available production history. Depending on the amount of production history available, the combined deterministic-stochastic model that provides the best fit can vary. It is therefore recommended that all possible combinations of the deterministic and stochastic models be applied to the available production history data. This is in order to obtain more confidence in the conclusions related to the reserve estimates and uncertainty bounds. The novelty of this methodology relies in using multiple combinations of DCA-Bayesian models to achieve accurate reserve estimates and narrow uncertainty bounds. The paper can help assess shale plays as most of the shale plays are in the early stages of production when the reserve estimations are carried out.

Analysts increasingly have used probabilistic approaches to evaluate the uncertainty in reserves estimates based on a decline curve analysis. This is because the results represent statistical analysis of historical data that usually possess significant amounts of noise. Probabilistic approaches usually provide a distribution of reserves estimates with three confidence levels (P10, P50 and P90) and a corresponding 80% confidence interval. The question arises: how reliable is this 80% confidence interval? In other words, in a large set of analyses, is the true value of reserves contained within this interval 80% of the time? Our investigation indicates that it is common in practice for true values of reserves to lie outside the 80% confidence interval much more than 20% of the time using traditional statistical analyses. This indicates that uncertainty is being underestimated, often significantly. Thus, the challenge in probabilistic reserves estimation using a decline curve analysis is not only how to appropriately characterize probabilistic properties of complex production data sets, but also how to determine and then improve the reliability of the uncertainty quantifications. This thesis presents an improved methodology for probabilistic quantification of reserves estimates using a decline curve analysis and practical application of the methodology to actual individual well decline curves. The application of our proposed new method to 100 oil and gas wells demonstrates that it provides much wider 80% confidence intervals, which contain the true values approximately 80% of the time. In addition, the method yields more accurate P50 values than previously published methods. Thus, the new methodology provides more reliable probabilistic reserves estimation, which has important impacts on economic risk analysis and reservoir management.

Accurately estimating hydrocarbon reserves is important, because it affects every phase of the oil and gas business. Unfortunately, reserves estimation is always uncertain, since perfect information is seldom available from the reservoir, and uncertainty can complicate the decision-making process. Many important decisions have to be made without knowing exactly what the ultimate outcome will be from a decision made today. Thus, quantifying the uncertainty is extremely important. Two methods for estimating original hydrocarbons in place (OHIP) are volumetric and material balance methods. The volumetric method is convenient to calculate OHIP during the early development period, while the material balance method can be used later, after performance data, such as pressure and production data, are available. In this work, I propose a methodology for using a Bayesian approach to quantify the uncertainty of original gas in place (G), aquifer productivity index (J), and the volume of the aquifer (W[subscript i]) as a result of combining volumetric and material balance analysis in a water-driven gas reservoir. The results show that we potentially have significant non-uniqueness (i.e., large uncertainty) when we consider only volumetric analyses or material balance analyses. By combining the results from both analyses, the non-uniqueness can be reduced, resulting in OGIP and aquifer parameter estimates with lower uncertainty. By understanding the uncertainty, we can expect better management decision making.

Proved reserves estimation is a crucial process since it impacts aspects of the petroleum business. By definition of the Society of Petroleum Engineers, the proved reserves must be estimated by reliable methods that must have a chance of at least a 90 percent probability (P90) that the actual quantities recovered will equal or exceed the estimates. Decline curve analysis, DCA, is a commonly used method; which a trend is fitted to a production history and extrapolated to an economic limit for the reserves estimation. The trend is the "best estimate" line that represents the well performance, which corresponds to the 50th percentile value (P50). This practice, therefore, conflicts with the proved reserves definition. An exponential decline model is used as a base case because it forms a straight line in a rate-cum coordinate scale. Two straight line fitting methods, i.e. ordinary least square and error-in-variables are compared. The least square method works better in that the result is consistent with the Gauss-Markov theorem. In compliance with the definition, the proved reserves can be estimated by determining the 90th percentile value of the descending order data from the variance. A conventional estimation using a principal of confidence intervals is first introduced to quantify the spread, a difference between P50 and P90, from the variability of a cumulative production. Because of the spread overestimation of the conventional method, the analytical formula is derived for estimating the variance of the cumulative production. The formula is from an integration of production of rate over a period of time and an error model. The variance estimations agree with Monte Carlo simulation (MCS) results. The variance is then used further to quantify the spread with the assumption that the ultimate cumulative production is normally distributed. Hyperbolic and harmonic models are also studied. The spread discrepancy between the analytics and the MCS is acceptable. However, the results depend on the accuracy of the decline model and error used. If the decline curve changes during the estimation period the estimated spread will be inaccurate. In sensitivity analysis, the trend of the spread is similar to how uncertainty changes as the parameter changes. For instance, the spread reduces if uncertainty reduces with the changing parameter, and vice versa. The field application of the analytical solution is consistent to the assumed model. The spread depends on how much uncertainty in the data is; the higher uncertainty we assume in the data, the higher spread.

In the last two years, due in part to the collapse of natural gas prices, the oil industry has turned its focus from shale gas exploration to shale oil/tight oil. Some of the important plays under development include the Bakken, Eagle Ford, and Niobrara. New decline curve methods have been developed to replace the standard Arps model for use in shale gas wells, but much less study has been done to verify the accuracy of these methods in shale oil wells. The examples that I investigated were Arps with a 5% minimum decline rate as well as the stretched exponential model (SEPD) and the Duong method. There is a great amount of uncertainty about how to calculate reserves in shale reservoirs with long multi-fractured horizontals, since these wells have not yet been produced to abandonment. Although the Arps model can reliably describe conventional reservoir production decline, it is still uncertain which empirical decline curve method best describes a shale oil well to get a rapid assessment of expected recovery. My focus began in the oil window of the Eagle Ford, but I ultimately chose to study the Elm Coulee field (Bakken formation) instead to see what lessons an older tight oil play could lend to newer plays such as the Eagle Ford. Contrary to existing literature, I have found evidence from diagnostic plots that many horizontal wells in the Elm Coulee that began producing in 2006 and 2007 have entered boundary-dominated flow. In order to accommodate boundary flow I have modified the Duong and SEPD methods such that once boundary-dominated flow begins the decline is described by an Arps curve with a b-value of 0.3. What I found from hindcasting was that early production history, up to six months, is generally detrimental to accurate forecasting in the Elm Coulee. This was particularly true for the Arps with 5% minimum decline or the Duong method. Early production history often contains apparent bilinear flow or no discernible trend. There are many possible reasons for this, particularly the rapid decrease in bottomhole pressure and production of fracture fluid. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/151644

This thesis improves oil- and gas-well profitability by quantifying the uncertainty of the production-forecasting process, using probabilistic machine learning (ML) techniques. A Bayesian Neural Network successfully modelled a complex shale gas reservoir system (Eagle Ford), generating a production forecast with 5% mean absolute percent error. This result is 10%-35% more accurate than traditional decline curve analysis. These forecasts also quantified the epistemic and aleatory uncertainties, providing plausible probabilistic P10 and P90 values. This range provides analysts with the capability of making informed strategic decisions that consider risk. Next, the model was applied to predict reserves (estimated ultimate recovery) and the underlying reservoir quality. These predictions were combined with unsupervised learning techniques (Gaussian Mixture Modelling), creating gas and oil sweet-spot maps. Finally, this workflow's robustness was demonstrated by artificially reducing data by 93%; indeed, the algorithm could reproduce the full-dataset results with a 71%-91% Pearson correlation, despite this reduction. Supporting this workflow creation is an evaluation of relevant research, data processing, feature engineering, documentation of the probabilistic ML structure, and discussion of model performance using systems analysis.