W. John Lee

Application of Pseudotime to Buildup Test Analysis of Low-Permeability Gas Wells With Long-Duration Wellbore Storage Distortion

An imporved method is presented for analyzing pressure transient tests in low-permeability gas wells that is based on a nonlinear form of the diffusivity equation rather than the linear form associated with liquid flow. This review delineates a theoretical basis for plotting pseudopressure changes against elapsed pseudotime to obtain a curve that in some cases corresponds to a type curve derived for a slightly compressible liquid with constant wellbore storage. Computer simulated tests and field data both support the theoretical results, suggesting that (1) the use of both pseudotime and pseudopressure yields linear equations for modeling gas flow in reservoirs and (2) types curves developed for slightly compressible liquids with unchanging wellbore storage constants can be used for gas well tests following large pressure drawdowns if analyzed using pseudotime and pseudopressure.

Quantification of Uncertainty in Reserve Estimation From Decline Curve Analysis of Production Data for Unconventional Reservoirs

Decline curve analysis is the most commonly used technique to estimate reserves from historical production data for the evaluation of unconventional resources. Quantifying the uncertainty of reserve estimates is an important issue in decline curve analysis, particularly for unconventional resources since forecasting future performance is particularly difficult in the analysis of unconventional oil or gas wells. Probabilistic approaches are sometimes used to provide a distribution of reserve estimates with three confidence levels (P10, P50, and P90) and a corresponding 80% confidence interval to quantify uncertainties. Our investigation indicates that uncertainty is commonly underestimated in practice when using traditional statistical analyses. The challenge in probabilistic reserve estimation 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. In this paper, we present an advanced technique for the probabilistic quantification of reserve estimates using decline curve analysis. We examine the reliability of the uncertainty quantification of reserve estimates by analyzing actual oil and gas wells that have produced to near-abandonment conditions, and also show how uncertainty in reserve estimates changes with time as more data become available. We demonstrate that our method provides a more reliable probabilistic reserve estimation than other methods proposed in the literature. These results have important impacts on economic risk analysis and on reservoir management.

Inverted Hockey Stick Method Quantifies Price Uncertainty in Petroleum Investment Evaluation

Abstract In this paper, we present a new method for quantifying the uncertainty of economic projections due to uncertainty in future oil prices. Traditionally, the petroleum industry has employed what are known as “hockey stick” price forecasts, i.e., monotonically increasing price profiles, in economic calculations to evaluate investment opportunities. Calculations are often run using most-likely, optimistic, and pessimistic price profiles in an attempt to quantify the uncertainty in the resulting economic indicators. These conventional hockey stick methods significantly underestimate uncertainty because they do not reproduce the volatility inherent in oil prices. Stochastic methods that attempt to model price volatility have been used successfully and indicate that there is considerably more uncertainty in oil and gas development projects than has been previously recognized. However, many operators do not use stochastic methods for modeling oil prices, most likely because they require more time and effort to implement than conventional methods. The Inverted Hockey Stick method presented herein is similar to conventional methods in that only three price realizations are run to quantify uncertainty. However, the high and low cases are designed to better capture the range of possible future price paths. Uncertainty ranges for economic indicators predicted by the new method are comparable to 70–95% probability ranges predicted by the stochastic bootstrap method, significantly greater than the 32–42% ranges predicted by conventional methods. This new method can be easily incorporated into existing economic modeling systems. Recognition of the greater uncertainty in oil and gas investment opportunities, both upside as well as downside, should improve investment decision making.

Quantification of Uncertainty by Combining Forecasting with History Matching

Abstract Quantifying uncertainty in production forecasts is critical to making good reservoir management decisions, particularly for many current investment opportunities that require intensive technology and large investments, and that may have marginal profitability indicators. Reservoir studies are conducted to support decision making, but reservoir management decisions must often be made before completion of these studies. This paper presents a new approach to reservoir studies that combines production forecasting with history matching. The approach provides preliminary production forecasts much earlier in reservoir studies. More importantly, the approach provides estimates of uncertainty associated with the forecasts. This is accomplished by using the mismatch of history match runs to weight corresponding forecast runs. We illustrate application of the method to the 8-Sand reservoir in the Green Canyon 18 field, Gulf of Mexico. We observed that, as the accuracy of the model increased during the history match, the uncertainty of forecasted reserves decreased and the distribution of reserves stabilized. Early forecasts and associated estimates of uncertainty provided by our new method can be quite valuable to management in making investment decisions.

A Practical Nonlinear Regression Technique for Horizontal Well Test Interpretation

Abstract A practical nonlinear regression technique for analysis of horizontal well pressure transient tests is presented. This technique can provide accurate and reliable estimation of well-reservoir parameters if downhole flow rate data are available. In situations without flow rate measurement, reasonably reliable parameter estimation can be achieved by using the detected flow rate from blind deconvolution. This technique has the advantages of eliminating the need for estimation of the wellbore storage coefficient and providing reasonable estimates of effective wellbore length. It provides a practical tool for enhancement of horizontal well test interpretation, and its practical applicability is illustrated by synthetic and actual field cases.

Calibration improves uncertainty quantification in production forecasting

Despite recent advances in uncertainty quantification, the petroleum industry continues to underestimate the uncertainties associated with reservoir production forecasts. This paper describes a calibration process that can improve quantification of uncertainties associated with reservoir performance prediction. Existing methods underestimate uncertainty because they fail to account for all, and particularly unknown, factors affecting reservoir performance and because they do not investigate all combinations of reservoir parameter values. However, the primary limitation of existing methods is that their reliability cannot be verified because the testing of an estimate of uncertainty from existing methods yields only one sample for what is inherently a statistical result. Verification and improvement of uncertainty estimates can be achieved with calibration – comparison of actual performance with previous uncertainty estimates and then using the results to scale subsequent uncertainty estimates. Calibration of uncertainty estimates can be achieved with a more frequent, if not continuous, process of data acquisition, model calibration, model prediction and uncertainty assessment, similar to the process employed in weather forecasting. Improved ability to quantify production forecast uncertainty should result in better investment decision making and, ultimately, increased profitability.

Quantification of Uncertainty in Reserves Estimation From Decline Curve Analysis of Production Data for Unconventional Reservoirs

Decline curve analysis is the most commonly used technique to estimate reserves from historical production data for evaluation of unconventional resources. Quantifying uncertainty of reserve estimates is an important issue in decline curve analysis, particularly for unconventional resources since forecasting future performance is particularly difficult in analysis of unconventional oil or gas wells. Probabilistic approaches are sometimes used to provide a distribution of reserve estimates with three confidence levels (P10, P50 and P90) and a corresponding 80% confidence interval to quantify uncertainties. Our investigation indicates that uncertainty is commonly underestimated in practice when using traditional statistical analyses. The challenge in probabilistic reserves estimation 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. In this paper, we present an advanced technique for probabilistic quantification of reserve estimates using decline curve analysis. We examine the reliability of uncertainty quantification of reserve estimates by analyzing actual oil and gas wells that have produced to near-abandonment conditions, and also show how uncertainty in reserves estimates changes with time as more data become available. We demonstrate that our method provides more reliable probabilistic reserves estimation than other methods proposed in the literature. These results have important impacts on economic risk analysis and on reservoir management.Copyright

Probabilistic Assessment of World Recoverable Shale Gas Resources

Many shales previously thought of as only source rocks are now recognized as self-sourcing reservoirs that contain large volumes of natural gas and liquid hydrocarbons that can be produced using horizontal drilling and hydraulic fracturing. However, shale gas resources and development economics are uncertain, and these uncertainties beg for a probabilistic solution. Our objective was to probabilistically determine the distribution of technically recoverable resources (TRR) and shale original gas in place (OGIP) in highly uncertain and risky shale gas reservoirs for seven world regions. To assess technically recoverable resources, we used the distribution of recovery factors from shale gas reservoirs. We developed a software, Unconventional Gas Resource Assessment System (UGRAS), which integrates Monte Carlo simulation with an analytical reservoir simulator to establish the probability distribution of OGIP and TRR. We used UGRAS to evaluate the most productive shale gas plays in the United States, including the Barnett, Eagle Ford, Marcellus, Fayetteville, and Haynesville shales, and derived a representative distribution of recovery factors for shale gas reservoirs. The recovery factors for the five shale gas plays follow a general Beta distribution with a mean value of 25%. Finally, we extended the distribution of recovery factors gained from our analyses of shale gas plays in the U.S. to estimate technically recoverable shale-gas resources for the seven world regions. Total technically recoverable shale gas resources are estimated to range from 4,000 Tcf (P90) to 24,000 Tcf (P10). UGRAS is a robust tool that may be used to evaluate and rank shale-gas resources worldwide. This work provides important statistics for the five most productive shale-gas plays in the United States. Results of this work verify the existence of significant technically recoverable shale gas resources worldwide and can help industry better target its exploitation efforts in shale-gas plays.

Advanced Deconvolution Technique for Analyzing Multirate Well Test Data

Deconvolution allows the test analyst to estimate the constant-rate transient pressure response of a reservoir-well system, and assists us in system identification and parameter estimation. Unfortunately, deconvolution amplifies the noise contained in data. Often, we cannot identify the reservoir system from deconvolved results owing to solution instability caused by noise in measured data. We previously presented a deconvolution technique based on the fast Fourier transform that we applied to a single buildup or drawdown period. In this paper, we extend our previous work and apply the deconvolution technique based on the fast Fourier transform to arbitrarily changing rate profiles such as multirate tests. The deconvolution results, which represent a constant-rate pressure drawdown response spanning the entire duration of the test, can provide helpful insight into the correct reservoir description. We have improved our original deconvolution method in number of ways, particularly with the introduction of an iterative algorithm that produces stable deconvolution results. We demonstrate application of our deconvolution method to analysis of synthetic and field examples, including both flow and shut-in periods. Our deconvolution method can efficiently reproduce the characteristic responses of the reservoir-well system and increase our confidence in parameter estimates.

Petroleum Engineering Education: The Road Ahead - A Summary of Major Actions at CPEE 2000

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s).