This work presents the various probabilistic methodology for forecasting petroleum production in shale reservoirs. Two statistical methods are investigated, Bayesian and frequentist, combined with various decline curve deterministic models. A robust analysis of well-completion properties and how they affect the production forecast is carried out. Lastly, a look into the uncertainties introduced by the statistical methods and the decline curve models are investigated to discover any correlation and plays that otherwise would not be apparent. We investigated two Bayesian methods - Absolute Bayesian Computation (ABC) and GIBBS sampler - and two frequentist methods - Conventional Bootstrap (BS) and Modified Bootstrap (MBS). We combined these statistical methods with five empirical models - Arps, Duong, Power Law Model (PLE), Logistic Growth Model (LGA), and Stretched Exponential Decline Model (SEPD) - and an analytical Jacobi 2 theta model. This allowed us to make a robust comparison of all these approaches on various unconventional plays across the United States, including Permian, Marcellus, Eagle Ford, Haynesville, Barnett, and Bakken shale, to get detailed insight on how to forecast production with minimal prediction errors effectively. Analysis was carried out on a total of 1800 wells with varying production history data lengths ranging from 12 to 60 months on a 12-month increment and a total production length of 96 months. We developed a novel approach for developing and integrating informative model parameter priors into the Bayesian statistical methods. Previous work assumed a uniform distribution for model parameter priors, which was inaccurate and negatively impacted forecasting performance. Our results show the significant superior performance of the Bayesian methods, most notably at early hindcast size (12 to 24 months production history). Furthermore, we discovered that production history length was the most critical factor in production forecasting that leveled the performance of all probabilistic methods regardless of the decline curve model or statistical methodology implemented. The novelty of this work relies on the development of informative priors for the Bayesian methodologies and the robust combination of statistical methods and model combination studied on a wide variety of shale plays. In addition, the whole methodology was automated in a programming language and can be easily reproduced and used to make production forecasts accurately.

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.

Predicting the production rate and ultimate production of shale resource plays is critical in order to determine if development is economical. In the absence of production from the Shublik Shale, Alaska, Arps' decline model and other newly proposed decline models were used to analyze production data from oil producing wells in the Eagle Ford Shale, Texas. It was found that shales violated assumptions used in Arps' model for conventional hydrocarbon accumulations. Newly proposed models fit the past production data to varying degrees, with the Logistic Growth Analysis (LGA) and Power Law Exponential (PLE) models making the most conservative predictions and those of Duong's model falling in between LGA and PLE. Using a regression coefficient cutoff of 95%, we see that the LGA model fits the production data (both rate and cumulative) from 81 of the 100 wells analyzed. Arps' hyperbolic and the LGA equation provided the most optimistic and pessimistic reserve estimates, respectively. The second part of this study investigates how the choice of residual function affects the estimation of model parameters and consequent remaining well life and reserves. Results suggest that using logarithmic rate residuals maximized the likelihood of Arps' equation having bounded estimates of reserves. We saw that approximately 75% of the well histories that were fitted using the logarithmic rate residual had hyperbolic b-values

Reserves estimation in an unconventional-reservoir setting is a daunting task because of geologic uncertainty and complex flow patterns evolving in a long-stimulated horizontal well, among other variables. To tackle this complex problem, we present a reserves-evaluation workflow that couples the traditional decline-curve analysis with a probabilistic forecasting frame. The stretched-exponential production decline model (SEPD) underpins the production behavior. Our recovery appraisal workflow has two different applications: forecasting probabilistic future performance of wells that have production history; and forecasting production from new wells without production data. For the new field case, numerical model runs are made in accord with the statistical design of experiments for a range of design variables pertinent to the field of interest. In contrast, for the producing wells the early-time data often need adjustments owing to restimulation, installation of artificial-lift, etc. to focus on the decline trend. Thereafter, production data of either new or existing wells are grouped in accord with initial rates to obtain common SEPD parameters for similar wells. After determining the distribution of model parameters using well grouping, the methodology establishes a probabilistic forecast for individual wells. We present a probabilistic performance forecasting methodology in unconventional reservoirs for wells with and without production history. Unlike other probabilistic forecasting tools, grouping wells with similar production character allows estimation of self-consistent SEPD parameters and alleviates the burden of having to define uncertainties associated with reservoir and well-completion parameters.

Decline curve analysis is widely applied for production forecasting in oil & gas industry. However, many models do not work for super-tight, unconventional wells with dominant fracture flows. Some novel decline models have been introduced for unconventional plays, but the transition time between the transient and pseudo-steady flow period is difficult to model with such pure empirical relations. Consequently, the decline projections are often inaccurate and furthermore, they are difficult to quantify the uncertainty associated with the predictions. To address these issues, a combined probabilistic approach is proposed that uses a dual-porosity semi-analytical decline model within an extended bootstrap framework in order to provide estimates for the P10, P50 and P90 production profiles. The probabilistic method employed in this research is a data-generative approach that employs modified bootstrap method to generate multiple decline model projections. The semi-analytical model is an approximate decline model that optimizes parameters describing flow in matrix-fracture systems using the observed production profile. In the proposed method, probabilistic approach and semi-analytical decline model are combined. The modified approach is compared to the performances developed with Arps' hyperbolic model. Both models are fitted by optimizing respective parameters and 50 synthetic data sets are used to draw confidence interval projections. The probabilistic approach is extended by proposing alternate blocking techniques - variance of the mean and analysis of the variance (ANOVA), in place of a scheme based on the autocorrelation exhibited by the decline data, originally implemented by other researchers. The cumulative production and forecast period production errors are calculated for these alternative schemes. For all proposed applications, two unconventional, horizontal oil wells are used to test the results. Both these wells exhibit sharp decline in production rate in the first few months that is related to fracture flow regimes. The results show that the proposed application of semi-analytical model with probabilistic approach significantly improved the projections. The implementation of alternate blocking techniques also show improvement in confidence interval projections, The resultant uncertainty distributions are more accurate and precise than those obtained using the autocorrelation based schemes. The combined results show that ANOVA blocking technique outperformed the other two techniques.

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