Uncertainty Analysis of Production Decline Data

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. This paper was prepared for the Gas Technology and Peripheral Waterflooding Symposium of the Society of Petroleum Engineers of AIME, to be held in Liberal, Kansas, November 14–15, 1968. Permission to copy is restricted to an abstract of not more than 300 words. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract A computerized technique, using a modified least-squares method to analyze wellhead shut in pressure vs. cumulative gas production decline curves, is presented for interpretation of low pressure, shallow (3,000 ft.) gas well reserves. A pilot study indicates benefits of the program to be (1) uniform method of analysis; (2) more accurate results; and (3) availability of the results for use in other computer applications. Analysis of several field case histories is presented. Introduction Decline curves provide a major tool to the evaluation engineer for the determination of individual well and total field reserves and often give some indication of the producing mechanism of the reservoir. The number of decline curves on file may number into the many thousands for a large company. Most companies generally update their curves on a yearly basis with the addition of current production data. Depending upon the number of curves, the process of updating and reinterpreting the decline curves may require the efforts of several people over a period of months. The use of decline curves for reserve evaluation work is most prevalent in fields which have been producing for a number of years. This criteria is necessary in order to accumulate sufficient production data from which to establish some rate of decline. The Hugoton Field in Kansas, Oklahoma and Texas and the West Panhandle Field in Texas are two such fields. Both of these fields have been producing natural gas for more than thirty year producing natural gas for more than thirty year Decline curves on the approximately 10,000 individual wells in the fields are extensive and well defined. Both fields produce from volumetric reservoirs within the Chase group of formations. The yearly task of updating and reinterpreting the decline curves of a major operator in these fields is a large undertaking. Last year a study was made to determine the feasibility of updating, analyzing and interpreting some 1,350 Hugoton and West Panhandle Field decline curves using a high speed digital computer.

Application of decline curve analysis in shale gas reservoirs is known to produce reserve estimates that are unphysical and/or unrealistic. It has been suggested that the assumptions inherent to these models may not always be valid in shale gas wells. For example, the boundary dominated flow period that leads to exponential decline may take years to develop in unconventional gas fields. Also, the impact of matrix adsorption/desorption processes on decline curve model parameters has not been fully investigated. To this end, we use a numerical simulator to understand key factors affecting production decline in shale gas reservoirs, and examine the appropriateness of decline curve based forecasting to model long-term flow behavior. A numerical model was constructed to simulate production from a horizontal well in a hydraulically fractured shale reservoir. Parameters varied in the evaluation include: (a) reservoir properties, (b) hydraulic fracture properties, (c) well properties, and (d) operational parameters. Ranges in values considered for the model parameters were obtained from published data on major shale-gas plays. Simulated gas production rate time histories were evaluated using standard decline curve analysis techniques. Our results indicate that long-term production estimates are most sensitive to hydraulic fracture and well characteristics, average pressure and permeability in the stimulated reservoir volume, and to a lesser degree on matrix flow and adsorption processes. Fitted decline curve model parameters generally exhibit time dependence, which affects the accuracy of ultimate recovery estimates with limited production data. The findings from this study suggest that although decline curve based reserve estimates may be appropriate under some conditions, it would be useful to apply a mechanistic (physics based) model for history matching production data and verify the results of decline curve analysis.

This paper demonstrates that decline curve analysis not only has a solid fundamental base but also provides a tool with more diagnostic power than has been suspected previously. The type curve approach provides unique solutions on which engineers can agree or shows when a unique solution is not possible with a type curve only. Introduction Rate-time decline curve extrapolation is one of the oldest and most often used tools of the petroleum engineer. The various methods used always have been regarded as strictly empirical and generally not scientific. Results obtained for a well or lease are subject to a wide range of alternate interpretations, mostly as a function of the experience and objectives of the evaluator. Recent efforts in the area of decline curve analysis have been directed toward a purely computerieed statistical approach, its basic objective being to arrive at a unique "unbiased" interpretation. As pointed out in a comprehensive review of the literature by Ramsay,1 "In the period from 1964 to date (1968), several additional papers were published which contribute to the understanding of decline curves but add little new technology." A new direction for decline curve analysis was given by Slider2 with his development of an overlay method to analyze rate-time data. Because his method was rapid and easily applied, it was used extensively by Ramsay in his evaluation of some 200 wells to determine the distribution of the decline curve exponent b. Gentry's3 Fig. 1 displaying the Arps4 exponential, hypbolic, and harmonic solutions all on one curve also could be used as an overlay to match all of a well's decline data. However, he did not illustrate this in his example application of the curve. The overlay method of Slider is similar in principle to the log-log type curve matching procedure presently being employed to analyze constant-rate pressure buildup and drawdown data.5–9 The exponential decline, often used in decline curve analysis, readily can be shown to be a long-time solution of the constant-pressure.10–13 It followed then that a log-log type curve matching procedure could be developed to analyze decline curve data.

Forecasting production from unconventional reservoirs is challenging because of the uncertainty that arises from intricate fracture networks, complex transport mechanisms, and convoluted flow configurations. The accuracy of decline curve analysis for such reservoirs has been questioned due to the limited amount of long-term production data available. That being so, some unconventional reservoirs, such as the Bakken and the Barnett, have produced for 15-20 years, providing an adequate amount of data to validate the accuracy of the hyperbolic decline curve method, shed light on proper parameters – b and Di, and determine the amount of production history necessary to trust regression techniques. To test this, an extensive and versatile regression analysis model was built in Python using least squares optimization to match specific durations of production data – first 6 months, first year, first two years, etc. The model outputs the optimal parameters – b and Di –to match the specific duration. Additionally, fixed b values from 0.5 to 1.5 are tested where only Di is optimized through the model. To understand how accurately the models predict production, they are validated against the most recent 5 years of data, which was not included in the matching period. For a statistically significant sample size, around 700 wells in the Bakken and 1800 wells in the Barnett with start dates between 2005 and 2010 were used. The results show that in order to have confidence in the model's ability to predict production, more than 3 years of production data must be available. If 3 years of data is not available, the hyperbolic exponent, b, should be set close to 1.0 for Bakken wells (and likely other unconventional liquid rich wells) and between 1.0 and 1.2 for Barnett wells (and likely other unconventional gas wells). Additionally, the initial nominal decline rate, Di, should be chosen in accordance with the hyperbolic exponent. Not only do these guidelines result in satisfactory, long-term predictions, but they mitigate any significant error influenced by the underlying relationships between b and Di. These curve-altering relationships induce both positive and negative impacts on the predictions. If b is improperly chosen, overestimation in late-life production profiles may ensue. Alternatively, if Di is improperly chosen, early-life production may be too high. Since production forecasting is a necessity for a company to determine its present value, this paper provides knowledge and guidance regarding forecasting procedures and parameter settings for North American unconventional operators. Using decline curve analysis to accurately predict oil and gas rates is pertinent to the longevity of these unconventional reservoirs.

Scope of this paper it to supply a workflow for gas shale simulation: starting from selection of best porosity model, through a definition of the most impacting phenomena hierarchy, it comes to a real application on gas shale in Barnett basin. Gas shale exploitation consists mainly in massive drilling campaign: this strategy can be successfully implemented where the costs per well is low, but elsewhere an accurate investigation including numerical modeling of gas shale reservoirs could be essential especially for defining optimal well spacing. We test several implementations of multi-porosity models (dual porosity, multi porosity, dual permeability). Even if all the models can simulate properly gas shale production we use "single porosity-like" that couples the advantage of dual permeability and single porosity models. Tests on synthetic cases have shown that gas production from shales is meanly affected by fracture spacing, proppant distribution inside induced and natural fractures, desorbed gas and in situ stress change. A real case of shale gas exploitation in Barnett shale is successfully matched by single porosity-like model, with SRV extension from microseismic mapping, 'water saturated' and pressurized hydraulic fracture, adsorption and change of in situ stress. Match of the water flow-back is obtained with non-equilibrium initialization: setting fracture cells with higher pressure and water saturation than surrounding ones. The matched case is then used as starting point for further analyses and sensitivities. Final goal is to provide a workflow for frontier basin where few production data are available with respect to what happens in USA and to calibrate decline curve for reserve estimation. Introduction Referring to gas shale means in 90% of cases talking about Barnett Basin (Texas, USA). They symbolize the ideal play with huge number of wells already producing and where the market condition gives the opportunity to massively apply available technology and to test new development strategies. Anyway uncertainties still remains. Decline curves analysis are largely used to assess reserves and future development plans, but reservoir simulation can give an added value adding more physics or controls compared to Decline Curves. As known, 3D simulation of gas shales is not a simple task because of complexity of storage and transport system, long water flow-back period, uncertain proppant distribution, gas desorption, etc..

Diverse techniques have been developed to improve the estimated reserves for boundary-dominated flow dry gas wells. The various methods developed and published in various journals on how to estimate reserves range from material balance techniques to decline curve analysis. Among the various techniques, decline curves are found quite accurate in predicting good gas performance in the absence of well-known reservoir parameters. There are basically two issues that practically arise in applying decline curve analysis, particularly in boundary-dominated flow dry gas wells. First, it has been noted that it is difficult to match a decline exponent, especially at an early stage of well depletion, even with worthy quality data. Secondly, decline exponent is not constant from observation, but changes with declining production. So, the study has provided a new method based on numerical curve fitting to accurately match the Arps’ decline curve function, even at the early depletion stage, and account for the changing decline exponent. Once the match objective is satisfied, future predictions can be made with a reasonable degree of assurance. Finally, the study showed that for the Arps’ decline equation to be valid, the decline exponent must be between 0 and 1.

Decline curves are fast methods to predict production behavior in oil and gas wells. Some of the notable decline curve methods are Arp’s, SEDM (Stretched Exponential Decline Model), Duong’s Model and Weibull decline curves. Available production history data can be used to fit any of these equations and future production decline can thus be extrapolated. However, when limited production data is available during early periods of well history, these equations could be fitted using inaccurate parameters leading to erroneous predictions. Also, the traditional decline curve analysis approach does not account for the complexities related to reservoir description and well completions.This study utilizes publicly available databases of the Eagle Ford formation to develop a novel predictive modeling methodology linking decline curve model parameters to well completion related variables that allows for the rapid generation of synthetic decline curves at potential new well locations. Modern machine learning algorithms such as Random Forests (RF), Support Vector Machines (SVM) and Multivariate Adaptive Regression Splines (MARS) can then be used to model the well decline behavior. Cross-Validation technique such as k-fold cross-validation can be used to quantify the predictive accuracy of these models when applied to new wells.First, production data are fitted to decline curve models to estimate the corresponding model parameters. Next, machine learning models are built for these parameters as a function of initial flow rate, various well completion parameters (i.e., number of hydraulic fracture stages, completed lengths, proppant and fracturing fluid amounts) and well location/depth parameters (i.e., well latitudes, longitudes, total vertical depth of heel and difference between total vertical depths of heel and toe of horizontal wells). These models are used to rapidly predict the decline curves for new or existing wells without the need for costly reservoir simulators. It has been found that accurate prediction of rate decline of new wells can be predicted using this methodology. This method can also predict ultimate recovery of a new well based on data collected from previous wells.To our knowledge, this is the first time machine learning algorithms have been used to predict the decline curve parameters and examine the relative performance of various decline curve models. The power and utility of our approach are demonstrated by successful prediction of the decline behavior of blind wells that were not incorporated in the analysis. We also examine the relative influences of various well design and location variables to determine the hidden correlations or interactions among them which are hard to decipher with other methods.

This research presents the selection of an appropriate decline curve analysis (DCA) methodology according to the transient production performance of a multi-fractured horizontal well in an unconventional gas field by using the cumulative production incline rate (IQp) The IQp introduced in this research is the change of cumulative production per unit time divided by the cumulative production. The IQp was confirmed for use as an indicator that could generalise and quantify a production decline through the analysis of well production data. The IQp values of eight and four DCA methods were applied to the production data generated by a reservoir simulation. The Duong method forecasted the production trends most accurately when the IQp exceeded 0.25%, while the YM-SEPD method was the most preferable for the rates below 0.05%. In addition, the analysis of production data for shale gas wells in Canada and the USA matched the simulation results, confirming that it would be reasonable to use the IQp in order to select a DCA method to forecast the production of unconventional gas wells. [Received: February 23, 2017; Revised: December 7, 2017; Accepted: December 9, 2017]

Empirical methods of decline-curve analysis for shale gas reservoirs: Review, evaluation, and application

An efficient and timesaving approach to hyperbolic-decline-curve analysis has been developed that has made it possible to determine the hyperbolic b exponents characterized by thousands of wells. After extensive use of the technique, the authors concluded that the range of the b exponent previously prescribed by Arps is too narrow.

Summary This paper introduces an approach for the impact of skin factor on the decline curve analysis of hydraulically fractured reservoirs. The objective is to consider this impact in the production forecasting and the ultimate recovery estimation. The approach focuses on reducing the uncertainties that could be raised from this impact on the production history and increasing the accuracy of the predicted flow rates. It proposes an easy and promising tool for the decline curve analysis that could be applied confidently to different oil- and gas-producing wells and different reservoirs. This approach utilizes the rate-normalized flow rate derivative β behavior of the fractured reservoirs. This derivative demonstrates a constant behavior with time for each flow regime when the production history has not undergone the impact of the skin factor. However, the constant behavior no longer exists when this impact has influenced the production history. Instead, a power-law type model governs the relationship between the flow rate derivative and production time. New analytical flow rate decline curve models, exponential-type, are derived from the flow rate derivative power-law type models for the flow regimes. Different models for calculating the skin factor are developed for the three linear flow regimes that could be observed during the transient state flow conditions. The proposed flow rate models are used to simulate the production history and forecast the future performance. Moreover, the hydraulic fracture conductivity can be calculated using these models as well as the flow rate loss caused by skin factor. Several case studies are examined by the proposed approach where the production history is used to characterize the dominant flow regimes. The study has reached several observations and conclusions. The impact of skin factor is seen clearly throughout transient state flow regimes; however, this impact declines sharply before reaching pseudosteady-state flow (boundary-dominated flow regime). The impact of the skin factor alternates the constant behavior of the flow rate derivative with time to a power-law type relationship. A straight line of a slope (0.5) is diagnosed during hydraulic fracture and formation linear flow regime on the log-log plot of the flow rate derivative β and time, while the bilinear flow regime demonstrates a straight line of a slope (0.25). Because of the skin factor, exponential decline curve models replace the power-law type models of the flow rate during the abovementioned flow regimes. These models exhibit an excellent match between the calculated flow rate and the production history. The maximum flow rate loss occurs during very early production time even though the skin factor during this time is less than the intermediate production time. This study presents a novel approach for the decline curve analysis taking into account the impact of skin factor. The novelty is represented by considering the flow regimes in the production forecasting of hydraulically fractured reservoirs. This approach is smoothly applied to predict the future performance with no need to know the wellbore and reservoir parameters. It can be used to predict the declining flow rate for a constant or varied bottomhole flowing pressure.

Using available data from existing wells to plan new wells is standard practice in development of unconventional natural gas resources. However, available data may frequently contain hidden patterns that are not easily spotted. Uncovering such patterns could help provide guidance for new wells by answering questions such as the following: Which wells, for which data are available, behave similarly? What do similarly behaving wells have in common? How can this information be used for new wells? If some existing wells are known not to perform satisfactorily, what are the underlying reasons? How can poor performance be avoided in new wells? In this work, we are proposing an approach addressing these questions. Production data from multiple wells are supplied to principal component analysis (PCA) data pool. The so-called scores and loadings associated with principal components (PCs) are computed, and subsequent comparison of PCs can be used to reveal clusters of similarly behaving wells and their underlying distinguishing features. The data is further explored by estimating decline curve parameters using power-law exponential decline curve q(t)=Qiexp(−D^itn). Once production data from multiple wells are available, values of the parameters q^i,D^i,n are estimated for each well and then correlations between available well and formation parameters such as permeability, fracture conductivity, fracture half-length, aspect ratio, drainage area, zone thickness and cumulative gas in place in drainage area; and decline curve parameters are obtained using partial least square regression (PLSR). These correlations can be used to predict production behavior of new wells if well parameters are known. Moreover, they can guide the location, geometry, and stimulation of new wells. The proposed analysis was performed on twelve wells from the Holly Branch gas field, for which data were available. The analysis identified one cluster of nine wells behaving similarly, and three distinct wells. The difference between these wells was ascribed mainly to high fracture conductivity, permeability, and small fracture half length. Correlations for decline curve parameters were obtained with reasonable R-squared value. The proposed methodology can be used as a decision making tool that employs various data from existing wells to guide decisions on the geometry and stimulation of new wells in unconventional gas field development.

This paper presents analysis techniques for post-transient gas flow at a constant flowing bottomhole pressure. Reservoir parameters can be estimated from production decline curve analysis using analytical solutions which are formulated in terms of real gas pseudopressure analysis. These techniques were applied to a field study of two small, low productivity gas reservoirs in Northern Tennessee. The production data for this field study was analyzed using decline curve analysis. The types of decline curve analysis used were: rate-time graphical, rate-time and cumulative-time non-linear least squares. Decline curve analysis by the use of type curves was attempted, but data scatter caused significant deviation of results when compared to the other types of decline curve analysis. The decline curve analysis results were then interpreted using an analytic reservoir model which did include pseudopressure analysis. This analysis was verified by a simulated real gas example which attempted to model producing conditions similar to those encountered in the field. The overall objective of the field study was to find correlations of reservoir parameters to measured production data. Several rate-reserve, rate-permeability/porosity-агеа ko A, and rate-permeability-thickness (kh) correlations were obtained from the results of the decline curve analysis. The best correlations were based on an average rate, q¯3, calculated from a well's first three months of production.

Capacitance-Resistance (CR) models have received renewed interest in the past few years as a fast alternative to reservoir simulation to model and predict complex water or gas floods in mature reservoirs. Using an analogy between reservoirs and electrical systems, CR models represent the interactions between wells through analytical solutions to an equivalent capacitor-resistor circuit. CR models do not require a geologic model and can be built with only production and injection data. When modeling fields with numerous wells and a long history, traditional reservoir simulation workflows are extremely time-consuming. The simplicity of CR models make them extremely attractive to quickly model and predict the behavior of these complex reservoirs. Current CR models are able to represent accurately the behavior of reservoirs under strong water or gas floods, where the injection is the main driving mechanism for production. In such cases, the production rates are strongly correlated to the injection rates and CR model are ideally suited to decipher these interactions. However, most reservoirs start with a period of primary depletion or many are exploited under a weak injection strategy, for which CR models are not ideally suited. Here, we propose to combine decline-curve (DC) analysis with a CR model in order to solve this shortcoming. Using the superposition principle, the contribution of primary depletion to production is represented by DC and the contribution of injection is represented by the CR model. After presenting the formulation and implementation of our DC-CR model, we demonstrate its performance on a deep naturally fractured carbonate reservoir under hydrocarbon gas and nitrogen injection. The reservoir has over 30 years of production history: 23 years of primary depletion and 8 years of gas and nitrogen injection. Using a one-year blind test, we demonstrate that the model is able to accurately predict the reservoir behavior.

While in reality production from unconventional reservoirs with nanoscale pores and complex systems has caused a dramatic increase in oil and gas production, little is known about an effective characterization let alone prediction of long-term performance of individual wells. These systems challenge our classical understanding of petroleum reservoirs developed over decades. In the meantime, and the absence of a full understanding of the source rock systems, some practitioners have resorted to using reservoir engineering tools and techniques for production forecasting from source rocks. These toots borrowed from engineering principles of conventional petroleum reservoirs do not include the peculiar nature of the source rock systems. This, of course, is a long stretch going from applying conceptual models for uniform pore space occupied by hydrocarbons and water, to systems where fractures, microfractures, present significant complications to understanding the physics of the flow in source rocks. In summary, the realm of producing from source rock is one of those examples where before a better understanding of the rock physics is developed, already in different play areas, we have witnessed the phenomenal growth of drilling and completion of thousands of wells over the last decade. Forecasting EUR (estimated ultimate Recovery) for individual wells producing from source rocks are essential in decision making at all levels. This is quite challenging particularly when only a few months of production data are available to predict the future. An urgent need in the industry has been using rapid methods for estimation of EUR's in the early life of any new well. These estimates have critical economic viability for business success and economic survival. To stay competitive and to provide attractive rates of return, companies prefer to drill in areas with the highest EUR's per well. Among the techniques in widespread use are the decline curves. These simple regression models are used to estimate up-front guidance regarding total recoverable volumes over a long period. In practice, any forecasting can help to establish the resource base for individual wells and the entire asset. But the question is the validity of such forecasts. Decline curve analysis is based on empirical observations of production decline. In using decline curves, we assume that reservoir conditions and operating conditions causing the historical decline continue unchanged during the forecast period. In this study, we include well production with 5 or more years of history and examine various decline models using the early history data to test the estimated performance vs. the actual performance. We have noted serious limitations on the use of such models.