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.

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.

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 recent years, production decline-curve analysis has become the most widely used tool in the industry for oil and gas reservoir production analysis. However, most curve analysis is done by computer today, promoting a "black-box" approach to engineering and leaving engineers with little background in the fundamentals of decline analysis. Advanced Production Decline Analysis and Application starts from the basic concept of advanced production decline analysis, and thoroughly discusses several decline methods, such as Arps, Fetkovich, Blasingame, Agarwal-Gardner, NPI, transient, long linear flow, and FMB. A practical systematic introduction to each method helps the reservoir engineer understand the physical and mathematical models, solve the type curves and match up analysis, analyze the processes and examples, and reconstruct all the examples by hand, giving way to master the fundamentals behind the software. An appendix explains the nomenclature and major equations, and as an added bonus, online computer programs are available for download. Understand the most comprehensive and current list of decline methods, including Arps, Fetkovich, Blasingame, and Agarwal-Gardner Gain expert knowledge with principles, processes, real-world cases and field examples Includes online downloadable computer programs on Blasingame decline type curves and normalized pseudo-pressure of gas wells

This study proposes a new, easily applied method to quantify uncertainty in production forecasts for a volumetric gas reservoir based on a material balance model (p/z vs. G [subscript] p). The new method uses only observed data and mismatches between regression values and observed values to identify the most probable value of gas reserves. The method also provides the range of probability of values of reserves from the minimum to the maximum likely value. The method is applicable even when only limited information is available from a field. Previous methods suggested in the literature require more information than our new method. Quantifying uncertainty in reserves estimation is becoming increasingly important in the petroleum industry. Many current investment opportunities in reservoir development require large investments, many in harsh exploration environments, with intensive technology requirements and possibly marginal investment indicators. Our method of quantifying uncertainty uses a priori information, which could come from different sources, typically from geological data, used to build a static or prior reservoir model. Additionally, we propose a method to determine the uncertainty in our reserves estimate at any stage in the life of the reservoir for which pressure-production data are available. We applied our method to San Juan reservoir at Santa Rosa Field, Venezuela. This field was ideal for this study because it is a volumetric reservoir for which the material balance method, the p/z vs. G[subscript] p plot, appears to be appropriate.

Today everyone seems to agree that ultra-low permeability and shale reservoirs have become the potentials to transform North America's oil and gas industry to a new phase. Unfortunately, transient flow is of long duration (perhaps life of the well) in ultra-low permeability reservoirs, and traditional decline curve analysis (DCA) models can lead to significantly over-optimistic production forecasts without additional safeguards. Stretched Exponential decline model (SEDM) gives considerably more stabilized production forecast than traditional DCA models and in this work it is shown that it produces unchanging EUR forecasts after only two-three years of production data are available in selected reservoirs, notably the Barnett Shale. For an individual well, the SEDM model parameters, can be determined by the method of least squares in various ways, but the inherent nonlinear character of the least squares problem cannot be bypassed. To assure a unique solution to the parameter estimation problem, this work suggests a physics-based regularization approach, based on critical velocity concept. Applied to selected Barnett Shale gas wells, the suggested method leads to reliable and consistent EURs. To further understand the interaction of the different fracture properties on reservoir response and production decline curve behavior, a series of Discrete Fracture Network (DFN) simulations were performed. Results show that at least a 3-layer model is required to reproduce the decline behavior as captured in the published SEDM parameters for Barnett Shale. Further, DFN modeling implies a large number of parameters like fracture density and fracture length are in such a way that their effect can be compensated by the other one. The results of DFN modeling of several Barnett Shale horizontal wells, with numerous fracture stages, showed a very good agreement with the estimated SEDM model for the same wells. Estimation of P90 reserves that meet SEC criteria is required by law for all companies that raise capital in the United States. Estimation of P50 and P10 reserves that meet SPE/WPC/AAPG/SPEE Petroleum Resources Management System (PRMS) criteria is important for internal resource inventories for most companies. In this work a systematic methodology was developed to quantify the range of uncertainty in production forecast using SEDM. This methodology can be used as a probabilistic tool to quantify P90, P50, and P10 reserves and hence might provide one possible way to satisfy the various legal and technical-society-suggested criteria.

ne of the most important aspects in the life-cycle of a petroleum well is understanding, and being able to reasonably predict, the total hydrocarbon output that a well will have through its producing life. The estimation of reserves has strong economic and legal implications that will not only determine whether a well-drilling plan is viable but also the worth of a company itself. This study aims to better understand the two primary production forecasting methods used in the petroleum industry: decline curve analyses and numerical reservoir simulations, and their ability to complement one another to make a better-informed production forecast when used together. Decline curve analyses have a heavy reliance on prior hydrocarbon production data which presents difficulty in forecasting during early-term behavior due to a lack of production data; however, reservoir simulations are stronger in early well-life because they are based more heavily on reservoir parameters. The objective is to use reservoir simulations to inform the decline curve's early time behavior, by informing parameters in their equations such as Dmin, while developing a correlational relationship between the two forecasting techniques that could be applied and translated to other reservoirs in the future. A decline curve analysis was performed on a three-well study area and Dmin values of 6%, 8%, and 10% were evaluated. The matching process of the decline curves heavily relied on the cumulative production in addition to the production rates, which used a thirty-day rolling average of the daily production data. Two equivalent numerical reservoir simulation models were built for the Eagle Ford which primarily used literature sourced values for the properties. The models were history matched to the observed data very well, though each model indicated different conclusions for a suggested Dmin value. Further compounding the results, the range of uncertainty in the matrix porosity property is larger than the range of the Dmin values. Due to this, the authors are not able to use the simulation models to inform parameters in decline curve analyses nor attempt to translate that relationship to other reservoirs.