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.

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.

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. / text

Unconventional reservoir systems can best be described as petroleum (oil and/or gas) accumulations which are difficult to be characterized and produced by conventional technologies. In this work we present the development of a systematic procedure to evaluate well performance in unconventional (i.e., low to ultra-low permeability) reservoir systems. The specific tasks achieved in this work include the following: ● Integrated Diagnostics and Analysis of Production Data in Unconventional Reservoirs: We identify the challenges and common pitfalls of production analysis and provide guidelines for the analysis of production data. We provide a comprehensive workflow which consists of model-based production analysis (i.e., rate-transient or model matching approaches) complemented by traditional decline curve analysis to estimate reserves in unconventional reservoirs. In particular, we use analytical solutions (e.g., elliptical flow, horizontal well with multiple fractures solution, etc.) which are applicable to wells produced in unconventional reservoirs. ● Deconvolution: We propose to use deconvolution to identify the correlation between pressure and rate data. For our purposes we modify the B-spline deconvolution algorithm to obtain the constantpressure rate solution using cumulative production and bottomhole pressure data in real time domain. It is shown that constant-pressure rate and constant-rate pressure solutions obtained by deconvolution could identify the correlation between measured rate and pressure data when used in conjunction. ● Series of Rate-Time Relations: We develop three new main rate-time relations and five supplementary rate-time relations which utilize power-law, hyperbolic, stretched exponential, and exponential components to properly model the behavior of a given set of rate-time data. These relations are well-suited for the estimation of ultimate recovery as well as for extrapolating production into the future. While our proposed models can be used for any system, we provide application almost exclusively for wells completed in unconventional reservoirs as a means of providing estimates of time-dependent reserves. We attempt to correlate the rate-time relation model parameters versus model-based production analysis results. As example applications, we present a variety of field examples using production data acquired from tight gas, shale gas reservoir systems.

Current models used to forecast production in unconventional oil and gas formations are often not producing valid results. When traditional decline curve analysis models are used in shale formations, Arps b-values greater than 1 are commonly obtained, and these values yield infinite cumulative production, which is non-physical.. Additional methods have been developed to prevent the unrealistic values produced, like truncating hyperbolic declines with exponential declines when a minimum production rate is reached. Truncating a hyperbolic decline with an exponential decline solves some of the problems associated with decline curve analysis, but it is not an ideal solution. The exponential decline rate used is arbitrary, and the value picked greatly effects the results of the forecast. A new empirical model has been developed and used as an alternative to traditional decline curve analysis with the Arps equation. The new model is based on the concept of logistic growth models. Logistic growth models were originally developed in the 1830s by Belgian mathematician, Pierre Verhulst, to model population growth. The new logistic model for production forecasting in ultra-tight reservoirs uses the concept of a carrying capacity. The carrying capacity provides the maximum recoverable oil or gas from a single well, and it causes all forecasts produced with this model to be within a reasonable range of known volumetrically available oil. Additionally the carrying capacity causes the production rate forecast to eventually terminate as the cumulative production approaches the carrying capacity. The new model provides a more realistic method for forecasting reserves in unconventional formations than the traditional Arps model. The typical problems encountered when using conventional decline curve analysis are not present when using the logistic model. Predictions of the future are always difficult and often subject to factors such as operating conditions, which can never be predicted. The logistic growth model is well established, robust, and flexible. It provides a method to forecast reserves, which has been shown to accurately trend to existing production data and provide a realistic forecast based on known hydrocarbon volumes. / text

[pt] Essa dissertação tem como objetivo apresentar e aplicar métodos para estimar probabilisticamente as reservas recuperáveis de petróleo de campos maduros (campos em fase de declínio), a partir dos dados históricos da produção (taxa de produção e tempo). Inicialmente é feita uma revisão bibliográfica de tópicos relevantes ao assunto e são apresentados os métodos de ajuste da curva de declínio e de estimação probabilística das reservas encontrados na literatura. Em seguida, são adaptadas a esses métodos algumas modificações consideradas relevantes para uma melhor precisão dos resultados e são desenvolvidos programas em linguagem VBA capazes de fazer a estimação probabilística das reservas recuperáveis e do tempo total de produção do campo desde o início do declínio. Por fim, são gerados resultados de um campo- produtor exemplo e feitas as devidas comparações entre as previsões determinísticas e as probabilísticas. / [en] This dissertation is intended to present and apply the probabilistic methods to estimate the recoverable reserves of mature oil fields (fields in the decline phase), from the historical production data (production rate and time). Initially, a bibliographical review is made and the methods of adjustment of the decline curve and probabilistic estimation of the reserves found in literature are presented. For greater precision, some modifications are made in these methods and programs are developed in Visual Basic. These programs are intended to obtain the probabilistic estimation of the recoverable reserves and the total production life of the field starting at the beginning of the decline phase. Finally, the results of a producing field are presented and the comparisons between the deterministic and the probabilistic forecasts are made.

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.

The Eagle Ford play in south Texas is currently one of the hottest plays in the United States. In 2012, the average Eagle Ford rig count (269 rigs) was 15% of the total US rig count. Assessment of the oil and gas resources and their associated uncertainties in the early stages is critical for optimal development. The objectives of my research were to develop a probabilistic methodology that can reliably quantify the reserves and resources uncertainties in unconventional oil and gas plays, and to assess Eagle Ford shale oil and gas reserves, contingent resources, and prospective resources. I first developed a Bayesian methodology to generate probabilistic decline curves using Markov Chain Monte Carlo (MCMC) that can quantify the reserves and resources uncertainties in unconventional oil and gas plays. I then divided the Eagle Ford play from the Sligo Shelf Margin to the San Macros Arch into 8 different production regions based on fluid type, performance and geology. I used a combination of the Duong model switching to the Arps model with b = 0.3 at the minimum decline rate to model the linear flow to boundary-dominated flow behavior often observed in shale plays. Cumulative production after 20 years predicted from Monte Carlo simulation combined with reservoir simulation was used as prior information in the Bayesian decline-curve methodology. Probabilistic type decline curves for oil and gas were then generated for all production regions. The wells were aggregated probabilistically within each production region and arithmetically between production regions. The total oil reserves and resources range from a P_(90) of 5.3 to P_(10) of 28.7 billion barrels of oil (BBO), with a P_(50) of 11.7 BBO; the total gas reserves and resources range from a P_(90) of 53.4 to P_(10) of 313.5 trillion cubic feet (TCF), with a P_(50) of 121.7 TCF. These reserves and resources estimates are much higher than the U.S. Energy Information Administration’s 2011 recoverable resource estimates of 3.35 BBO and 21 TCF. The results of this study provide a critical update on the reserves and resources estimates and their associated uncertainties for the Eagle Ford shale formation of South Texas.

Production of oil and gas from shale is often described as a revolution to energyproduction in North America. Since the beginning of this century the shale oilproduction has increased from practically zero to currently supply almost half of theU.S. oil production. This development is made possible by the technology ofhorizontal drilling and hydraulic fracturing. Since the production has not been ongoingfor that long, production data is still fairly limited in length and there are still largeuncertainties in many parameters, for instance production decline, lifespan, drainagearea, geographical extent and future technological development. More research isneeded to be able to estimate future production and resources with more certainty. At the moment shale oil is extracted only in North America but around the worldinvestigations are starting to assess if the conditions are suitable from shale oilextraction elsewhere. The global technically recoverable resource has been estimatedto 345 Gb, 10% of all global technically recoverable resources. Health andenvironmental aspects of shale oil and gas production have not yet been investigatedthoroughly and there is a risk that these parameters may slow down or limit thespreading of shale development. This report aims to examine production patterns of shale oil wells by applying declinecurve analysis. This analysis comprises of analyzing historical production data toinvestigate how the future production may develop. The area of the study is the EagleFord shale play in Texas, U.S. The goal is to fit decline curves to production data andthen use them for making estimates of future production in the Eagle Ford. The production in the shale oil wells included in the study reach their peak already within a few months after production starts. After this point, production is declining.After one year, production has decreased by 75% and after two years the productionis 87% of the peak production. The hyperbolic decline curve has a good fit toproduction data and in many cases the curve is close to harmonic. It is too early todetermine whether the alternative decline curve that is tested, the scaling declinecurve, has a better fit in the long term. The report also investigates how the density of the petroleum affects the declinecurve. The result is that lighter products decline faster than heavier. A sensitivity analysis is performed to illustrate how different parameters affect thefuture production development. In addition to the wells’ decline rate, the assumptionson the maximum number of wells, the maximal production and the rate at which newwells are added affect the ultimately recoverable resource. These parameters all havelarge uncertainties and makes resource estimations more difficult.

This study compares four recently developed decline curve methods and the traditional Arps or Fetkovich approach. The four methods which are empirically formulated for shale and tight gas wells are: 1. Power Law Exponential Decline (PLE). 2. Stretched Exponential Decline (SEPD). 3. Duong Method. 4. Logistic Growth Model (LGM). Each method has different tuning parameters and equation forms. The main objective of this work is to determine the best method(s) in terms of Estimated Ultimate Recovery (EUR) accuracy, goodness of fit, and ease of matching. In addition, these methods are compared against each other at different production times in order to understand the effect of production time on forecasts. As a part of validation process, all methods are benchmarked against simulation. This study compares the decline methods to four simulation cases which represent the common shale declines observed in the field. Shale wells, which are completed with horizontal wells and multiple traverse highly-conductive hydraulic fractures, exhibit long transient linear flow. Based on certain models, linear flow is preceded by bilinear flow if natural fractures are present. In addition to this, linear flow is succeeded by Boundary Dominated Flow (BDF) decline when pressure wave reaches boundary. This means four declines are possible, hence four simulation cases are required for comparison. To facilitate automatic data fitting, a non-linear regression program was developed using excel VBA. The program optimizes the Least-Square (LS) objective function to find the best fit. The used optimization algorithm is the Levenberg-Marquardt Algorithm (LMA) and it is used because of its robustness and ease of use. This work shows that all methods forecast different EURs and some fit certain simulation cases better than others. In addition, no method can forecast EUR accurately without reaching BDF. Using this work, engineers can choose the best method to forecast EUR after identifying the simulation case that is most analogous to their field wells. The VBA program and the matching procedure presented here can help engineers automate these methods into their forecasting sheets.