EBookClubs

Read Books & Download eBooks Full Online

EBookClubs

Read Books & Download eBooks Full Online

Book Production Decline Curves Using Data from California Oilfields

Download or read book Production Decline Curves Using Data from California Oilfields written by Ralph V. Higgins and published by . This book was released on 1971 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Advances in Geology and Resources Exploration

Download or read book Advances in Geology and Resources Exploration written by Ahmad Safuan Bin A Rashid and published by CRC Press. This book was released on 2022-09-19 with total page 1158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Geology and Resources Exploration provides a collection of papers resulting from the conference on Geology and Resources Exploration (ICGRED 2022), Harbin, China, 21-23 January, 2022. The primary goal of the conference is to promote research and developmental activities in geology, resources exploration and development, and another goal is to promote scientific information interchange between scholars from the top universities, business associations, research centers and high-tech enterprises working all around the world. The conference conducted in-depth exchanges and discussions on relevant topics such as geology, resources exploration, aiming to provide an academic and technical communication platform for scholars and engineers engaged in scientific research and engineering practice in the field of engineering geology, geological resources and geothermal energy. By sharing the status of scientific research achievements and cutting-edge technologies, this helps scholars and engineers all over the world to comprehend the academic development trend and to broaden research ideas. With a view to strengthen international academic research, academic topics exchange and discussion, and promoting the industrialization cooperation of academic achievements.

Book Advanced Production Decline Analysis and Application

Download or read book Advanced Production Decline Analysis and Application written by Hedong Sun and published by Gulf Professional Publishing. This book was released on 2015-02-12 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Book Informing the Modified Hyperbolic Decline Curve0  9s Minimum Decline Parameter with Numerical Simulation in Unconventional Reservoirs

Download or read book Informing the Modified Hyperbolic Decline Curve0 9s Minimum Decline Parameter with Numerical Simulation in Unconventional Reservoirs written by Zakary Kypfer and published by . This book was released on 2021 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Analysis of Production Decline Curves

Download or read book Analysis of Production Decline Curves written by Steven W. Poston and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the production characteristics and associated interpretation analyses of petroleum reservoirs in a complete, thorough, and consistent manner.

Book Master s Theses Directories

Download or read book Master s Theses Directories written by and published by . This book was released on 2002 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Education, arts and social sciences, natural and technical sciences in the United States and Canada".

Book Approximate Bayesian Computation for Probabilistic Decline Curve Analysis in Unconventional Reservoirs

Download or read book Approximate Bayesian Computation for Probabilistic Decline Curve Analysis in Unconventional Reservoirs written by Mohit Paryani and published by . This book was released on 2015 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Book Application of Probabilistic Decline Curve Analysis to Unconventional Reservoirs

Download or read book Application of Probabilistic Decline Curve Analysis to Unconventional Reservoirs written by Uchenna C. Egbe and published by . This book was released on 2022 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Uncertainty in Proved Reserves Estimation by Decline Curve Analysis

Download or read book Uncertainty in Proved Reserves Estimation by Decline Curve Analysis written by Woravut Apiwatcharoenkul and published by . This book was released on 2014 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Comparative Study of Decline Curve Analysis Methods Using a Lab scale Gas Reservoir

Download or read book Comparative Study of Decline Curve Analysis Methods Using a Lab scale Gas Reservoir written by Renzo Zamponi and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most effective approaches to estimate Original Gas in Place (OGIP) in dry gas volumetric reservoirs is the use of Decline Curve Analysis methods. The strength of these methods is that they rely on the availability of initial reservoir pressure and production data (flow-rate vs time), which are generally abundant, to generate estimates of original gas in place and future production predictions. Decline curve analysis methods are generally validated using field production data or data from computationally reservoir models. Some disadvantages of these validation approaches include the fact that gas reserves cannot be readily obtained from field data, and the accuracy of production predictions from reservoir models is subject to the model reliability. The aim of this study is to investigate the use of a lab-scale gas reservoir to generate reliable production data for a rigorous validation of decline curve analysis methods recently proposed in the literature. The methods under consideration are Flowing Material Balance (Mattar and Anderson, 2003), Ye and Ayala (2012, 2013), Stumpf and Ayala (2016), and Zhang and Ayala (2013, 2014a, 2014b). The lab-scale reservoir was designed, built and tested in a number of experiments, performed at different initial reservoir pressures and confining pressures. The production data obtained were used to estimate OGIP and compared against direct volumetric calculations. The divergence between these two values was called error. OGIP estimates showed good agreement with lab data, with variations in performance quality. The decline models proposed by Ye and Ayala (2012, 2013) and Zhang and Ayala (2013, 2014a, 2014b) yielded the most accurate estimations of Original Gas in Place, with an average error of 8.32 % for the first method and 8.67 % for the second. The Flowing Material Balance method was found to underperform for most lab conditions tested, showing an average error of 11.63 %.

Book Using Decline Curve Analysis  Volumetric Analysis  and Bayesian Methodology to Quantify Uncertainty in Shale Gas Reserve Estimates

Download or read book Using Decline Curve Analysis Volumetric Analysis and Bayesian Methodology to Quantify Uncertainty in Shale Gas Reserve Estimates written by Raul Alberto Gonzalez Jimenez and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Book Decline Curve Analysis in Unconventional Resource Plays Using Logistic Growth Models

Download or read book Decline Curve Analysis in Unconventional Resource Plays Using Logistic Growth Models written by Aaron James Clark and published by . This book was released on 2011 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Unsteady state Fluid Flow

Download or read book Unsteady state Fluid Flow written by E.J. Hoffman and published by Elsevier. This book was released on 1999-07-02 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ubiquitous examples of unsteady-state fluid flow pertain to the production or depletion of oil and gas reservoirs. After introductory information about petroleum-bearing formations and fields, reservoirs, and geologic codes, empirical methods for correlating and predicting unsteady-state behavior are presented. This is followed by a more theoretical presentation based on the classical partial differential equations for flow through porous media.Whereas these equations can be simplified for the flow of (compressible) fluids, and idealized solutions exist in terms of Fourier series for linear flow and Bessel functions for radial flow, the flow of compressible gases requires computer solutions, read approximations. An analysis of computer solutions indicates, fortuitously, that the unsteady-state behavior can be reproduced by steady-state density or pressure profiles at successive times. This will demark draw down and the transition to long-term depletion for reservoirs with closed outer boundaries.As an alternative, unsteady-state flow may be presented in terms of volume and surface integrals, and the methodology is fully developed with examples furnished. Among other things, permeability and reserves can be estimated from well flow tests.The foregoing leads to an examination of boundary conditions and degrees of freedom and raises arguments that the classical partial differential equations of mathematical physics may not be allowable representations. For so-called open petroleum reservoirs where say water-drive exists, the simplifications based on successive steady-state profiles provide a useful means of representation, which is detailed in the form of material balances.Unsteady-State Fluid Flow provides:• empirical and classical methods for correlating and predicting the unsteady-state behavior of petroleum reservoirs• analysis of unsteady-state behavior, both in terms of the classical partial differential equations, and in terms of volume and surface integrals• simplifications based on successive steady-state profiles which permit application to the depletion of both closed reservoirs and open reservoirs, and serves to distinguish drawdown, transition and long-term depletion performance.

Book A Study of Decline Curve Analysis in the Elm Coulee Field

Download or read book A Study of Decline Curve Analysis in the Elm Coulee Field written by Seth C Harris and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two years, due in part to the collapse of natural gas prices, the oil industry has turned its focus from shale gas exploration to shale oil/tight oil. Some of the important plays under development include the Bakken, Eagle Ford, and Niobrara. New decline curve methods have been developed to replace the standard Arps model for use in shale gas wells, but much less study has been done to verify the accuracy of these methods in shale oil wells. The examples that I investigated were Arps with a 5% minimum decline rate as well as the stretched exponential model (SEPD) and the Duong method. There is a great amount of uncertainty about how to calculate reserves in shale reservoirs with long multi-fractured horizontals, since these wells have not yet been produced to abandonment. Although the Arps model can reliably describe conventional reservoir production decline, it is still uncertain which empirical decline curve method best describes a shale oil well to get a rapid assessment of expected recovery. My focus began in the oil window of the Eagle Ford, but I ultimately chose to study the Elm Coulee field (Bakken formation) instead to see what lessons an older tight oil play could lend to newer plays such as the Eagle Ford. Contrary to existing literature, I have found evidence from diagnostic plots that many horizontal wells in the Elm Coulee that began producing in 2006 and 2007 have entered boundary-dominated flow. In order to accommodate boundary flow I have modified the Duong and SEPD methods such that once boundary-dominated flow begins the decline is described by an Arps curve with a b-value of 0.3. What I found from hindcasting was that early production history, up to six months, is generally detrimental to accurate forecasting in the Elm Coulee. This was particularly true for the Arps with 5% minimum decline or the Duong method. Early production history often contains apparent bilinear flow or no discernible trend. There are many possible reasons for this, particularly the rapid decrease in bottomhole pressure and production of fracture fluid. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/151644

Book Quantification of Production Recovery Using Probabilistic Approach and Semi analytical Model for Unconventional Oil Reservoirs

Download or read book Quantification of Production Recovery Using Probabilistic Approach and Semi analytical Model for Unconventional Oil Reservoirs written by Bong Joon Choi and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Simple Mechanistic Modeling of Recovery from Unconventional Oil Reservoirs

Download or read book Simple Mechanistic Modeling of Recovery from Unconventional Oil Reservoirs written by Babafemi Anthony Ogunyomi and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decline 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