Browsing by Subject "Decline curve analysis"
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Item Decline curve analysis in unconventional resource plays using logistic growth models(2011-08) Clark, Aaron James; Lake, Larry W.; Patzek, Tadeusz W.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.Item Developing a Vaca Muerta shale play : an economic assessment approach(2016-05) Sierra, Diego Ernesto; Ikonnikova, Svetlana; Fisher, W. L. (William Lawrence), 1932-A total of 450 production wells are in operation in Argentina’s Vaca Muerta shale formation as of February 2016, of which 90% were drilled since 2013. In order to assess the economic value of the vertical, directional, and horizontal wells and understand the potential future shale play development, a data-driven approach is developed. First, historical production data are used to derive a 10-year production forecast, using decline curve analysis. Then, well profitability is assessed applying a discounted cash flow model for a sample of vertical, directional, and horizontal wells in the Loma Campana field. Initial oil and gas production rates reached 172.56 BBL/day and 309.42 Mcf/day for the median vertical well, 392.81 BBL/day and 587.76 Mcf/day for the median directional well, and 456.75 BBL/day and 571.46 Mcf/day for the median horizontal well. Based on the production histories, 10-year cumulative oil and gas production is expected to reach 76,389 BBL and 97,772 Mcf for the median vertical well, 174,701 BBL and 261,402 Mcf for the median directional well, and 203,134 BBL and 254,154 Mcf for the median horizontal well. The median vertical well is found to have a negative net present value (NPV) for any possible discount rate, while median directional and horizontal wells can be expected to give NPV (10%) values of $0.41 and $1.14 million, respectively, under the current fiscal and contractual conditions in the country. Internal rates of return for the median directional and horizontal wells were found to be 15.15% and 26%, respectively, while their break-even oil prices at a 10% discount rate were found to be $54.65 and $47.23 per BBL, respectively. Thus, the production profiles and well economics assessment allows to suggest that directional and horizontal wells could be economically viable under the country’s current economic environment, including oil and gas price subsidies.Item Quantification of production recovery using probabilistic approach and semi-analytical model for unconventional oil reservoirs(2015-12) Choi, Bong Joon; Srinivasan, Sanjay; Sepehrnoori, Kamy, 1951-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.Item Simple mechanistic modeling of recovery from unconventional oil reservoirs(2015-05) Ogunyomi, Babafemi Anthony; Lake, Larry W.; Sepehrnoori, Kamy; Srinivasan, Sanjay; Jablonowski, Christopher J; Bickel, James EDecline curve analysis is the most widely used method of performance forecasting in the petroleum industry. However, when these techniques are applied to production data from unconventional reservoirs they yield model parameters that result in infinite (nonphysical) values of reserves. Because these methods were empirically derived the model parameters are not functions of reservoir/well properties. Therefore detailed numerical flow simulation is usually required to obtain accurate rate and expected ultimate recovery (EUR) forecast. But this approach is time consuming and the inputs in to the simulator are highly uncertain. This renders it impractical for use in integrated asset models or field development optimization studies. The main objective of this study is to develop new and “simple” models to mitigate some of these limitations. To achieve this object field production data from an unconventional oil reservoir was carefully analyzed to identify flow regimes and understand the overall decline behavior. Using the result from this analysis we use design of experiment (DoE), numerical reservoir simulation and multivariate regression analysis to develop a workflow to correlate empirical model parameters and reservoir/well properties. Another result from this analysis showed that there are at least two time scales in the production data (existing empirical and analytical model do not account for this fact). Double porosity models that account for the multiple time scales only have complete solutions in Laplace space and this make them difficult to use in optimization studies. A new approximate analytical solution to the double porosity model was developed and validated with synthetic data. It was shown that the model parameters are functions of reservoir/well properties. In addition, a new analytical model was developed based on the parallel flow conceptual model. A new method is also presented to predict the performance of fractured wells with complex fracture geometries that combines a fundamental solution to the diffusivity equation and line/surface/volume integral to develop solutions for complex fracture geometries. We also present new early and late time solutions to the double porosity model that provide explicit functions for skin and well/fracture storage, which can be used to improve the characterization of fractured horizontal wells from early-time production data.Item Uncertainty in proved reserves estimation by decline curve analysis(2014-12) Apiwatcharoenkul, Woravut; Lake, Larry W.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.