|Theme||Visible||Selectable||Appearance||Zoom Range (now: 0)|
Abstract Analysis of flow rate and pressure data, relies on the solution derived using the "constant rate" boundary condition. However, most of the time, production rates are variable. Therefore, superposition (convolution) must be used to make variable rates look like their equivalent constant rate solution. The classic way to apply the concept of superposition is to use Superposition-Time. It consists of a manipulation of time with respect to the changes in flow rates and flow durations. Valuable as that procedure is, it suffers from many pitfalls. For example, a) the resulting time is shuffled back and forth, and loses its physical significance, b) the selected superposition function makes the data tend to behave like that function (for example, radial flow superposition tends to make the data look like radial flow, while linear flow superposition tends to make the same data look like linear flow). As a result, without careful data diagnosis prior to analysis, flow regimes could be falsely interpreted, which results in misleading interpretation of well performance, and c) outliers are accentuated, resulting in a false interpretation of apparent validity. In this work, a new and innovative technique was developed using the well-known concept of superposition, but in an opposite manner. Rather than modify the time (as is done classically), we modified the rate. We derived a Superposition-Rate function which converts a variable rate situation to a constant rate equivalent. In the conventional approach to variable rate problems, we plot rate/pressure against Superposition-Time. In the approach developed in this paper, we plot Superposition-Rate directly against time (not Superposition-Time). The implementation of Superposition-Rate relies on the a priori knowledge of the flow regime. As most multi-stage hydraulically fractured horizontal wells are dominated by transient linear flow, linear Superposition-Rate was the primary focus of this paper. We developed the formulation of linear Superposition-Rate for both wells without skin and with skin. We created synthetic data sets to validate the use of Superposition-Rate. The synthetic data confirmed that Superposition-Rate successfully converts variable rate data to the equivalent constant rate solution. We also tested Superposition-Rate with real production data from shale gas reservoirs in North America. Superposition-Rate demonstrates the following advantages over Superposition-Time in production data analysis: The time scale is not modified in any way (Superposition-Time shuffles time in response to rate changes). This keeps all the data in the sequence of their occurrence, and results in a significant advantage in data-quality diagnostics. Superposition-Rate accentuates the transition from the linear flow straight line to boundary dominated flow as compared to Superposition-Time, thus aiding in the identification of flow regimes. Superposition-Rate eliminates the problem caused by Superposition-Time when outliers (i.e. abnormal production data) present. This is a significant improvement to data-quality diagnostics. With the use of Superposition-Rate outliers are not required to be removed prior to analysis.
Summary This research presents a new method to analyze production- and well-test data: the superposition rate. The method was developed from the well-accepted superposition principle. It is presented in a generalized form and is applicable to data in transient flow (including radial, linear, and bilinear), as well as in boundary-dominated flow (BDF). The superposition-rate method is validated by synthetic data generated from reservoir modeling. Moreover, a practical work flow of implementing the superposition rate in production-data and well-test analysis is presented. Finally, real-field examples are used to demonstrate the practicality of superposition rate. A comparison between the superposition-rate and superposition-time methods is presented. The superposition rate shows advantages over the superposition time. A key improvement of the superposition rate in quality diagnostics and data analysis is that it does not modify time scale. Consequently, the superposition rate keeps all production data in the sequence of their occurrence.
Summary In this study, we provide a detailed review and comparison of the various graphical methods, available in the literature, to interpret/analyze rate‐ and pressure‐transient data acquired from multistage hydraulically fractured horizontal wells (MHFHWs) completed in unconventional gas reservoirs. The methods reviewed in this study do not address complex transport mechanisms and complex fracture networks, but do address transient matrix linear flow (Ibrahim and Wattenbarger 2006; Nobakht and Clarkson 2012a, 2012b; Chen and Raghavan 2013) and boundary‐dominated flow (BDF). The methods for BDF are the contacted‐volume methods based on the ending times of linear flow (Wattenbarger et al. 1998; Behmanesh et al. 2015) and the flowing material‐balance (FMB) methods. The Agarwal‐Gardner FMB method (Agarwal et al. 1999) and the conventional FMB method involve plotting rate‐normalized pseudopressure vs. material‐balance pseudotime. We delineate the advantages and limitations associated with each method and identify the best methods of interpretation and analysis. Three different production modes—constant rate (CR), constant bottomhole pressure (BHP) (CBHP), and variable‐rate BHP—are considered. For comparison, various synthetic test data sets generated from a high‐resolution spectral gas simulator, which treats nonlinear gas flow rigorously and accurately to simulate rate‐transient data, is used. Both synthetic noise‐free and noisy‐rate pressure‐data sets considering wide ranges of initial reservoir pressure and BHP, as well as real‐field data sets, are used to compare the methods. For linear flow, the Nobakht‐Clarkson method (Nobakht and Clarkson 2012a, 2012b) yields the best results, although its use is tedious because it requires an iterative procedure. The Chen and Raghavan (2013) method for linear flow seems to provide results that are comparable with the Nobakht‐Clarkson method (Nobakht and Clarkson 2012b) but does not require an iterative procedure. The Ibrahim‐Wattenbarger method (Ibrahim and Wattenbarger 2006) for linear‐flow analysis always overestimates flow capacity compared with the other methods. Among the methods that discuss the ending time of linear flow, it was found that the unit‐impulse method from Behmanesh et al. (2015) provides the best results for predicting gas in place. For BDF, the results show that the Agarwal‐Gardner FMB method (Agarwal et al. 1999) is quite vulnerable to the error in rate/pressure data, whereas the conventional FMB method is more robust to noise and provides more accurate estimates of gas in place.
Abstract Production data are usually analyzed using typecurves. Production data are typically variable rates, whereas typecurves are typically "constant rate" solutions. Therefore, "superposition" must be used to convert the multiple rates into their constant rate equivalent, before typecurves can be used to determine the flow regime. For linear flow the kernel of the superposition function is square-root-time, for radial flow it is log-time and for boundary-dominated flow it is material-balance-time. When superposition is used, the appropriate function must be used. In practice, the dominant flow regime dictates the choice. However, the flow regimes can be determined only after typecurve matching. This creates a self-referencing procedure. In many situations, using square-root-time superposition makes the data look like linear flow, while using log-time makes it look like radial flow, and using material-balance-time makes it look like boundary dominated flow. This is self-defeating and can easily lead to the wrong diagnosis of flow regimes. In other situations, the choice of superposition function does NOT change the shape of the data, and the diagnosis tends to be unique. Numerous variable rates are investigated in an attempt to identify when superposition is safe, or which function distorts data the least. Superposition functions are more forgiving for the early time data, and therefore they are less likely to change the shape of the data significantly in well test analyses, whereas in production data analysis the focus is more on the late time data. Using an inappropriate superposition function can result in the wrong diagnosis of flow regimes and the wrong interpretation of production, and very critically, the wrong forecast of reserves. The choice of superposition function must be an "informed choice" by the analyst.