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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.
Abstract This research presents a new method to analyze production and well test data – the superposition-rate. The method was developed based on 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. The superposition-rate method is validated by synthetic data generated from reservoir modeling. Moreover, a practical workflow of implementing the superposition-rate in production data and well test analysis is presented. Last, real field examples are utilized to demonstrate the practicality of superposition-rate. A thorough 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. Introduction Analysis of rate and pressure data relies on the solutions of flow equation in porous media derived using constant boundary condition. All wells can exhibit one of the two constant boundary conditions: constant production rate or constant flowing pressure. For well testing operations, the flow period is typically controlled, and constant rate solutions are chosen to analyze well testing data. On the other hand, for production operations, the flowing pressure often declines rapidly and becomes constant during a prolonged period. As a result, constant pressure solutions are considered to be more useful in analyzing production data, particularly for wells in unconventional reservoirs. However, there are numerous situations where both rate and flowing pressure continuously decline, or make step changes (discontinuously) during well testing and production operations. These variable-rate/variable-pressure issues are typically addressed using superposition. The superposition principle is effective in converting variable-rate/variable-pressure data to its equivalent constant boundary solution. The classical way to apply the superposition principle is to use a time function, namely superposition-time. It involves manipulation of time in accordance with the changes in rates and flow durations. Valuable as this procedure is, it suffers from many disadvantages: for instance, after manipulation, the resulting time will have been shuffled back and forth. This makes the data's sequence difficult to be tracked and identified, and subsequently causes problems in data quality diagnostics. This is particularly evident in the presence of outliers.
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 Log-log superposition-time derivative plots are used to identify flow regimes in well tests with variable rate. The use of superposition time adjusts for the effect of the prior rate history, and (under some conditions) shows what the transient would have looked like if the test had been performed at a constant rate. In this report, I show that if these plots are used to interpret shut-in transients from diagnostic fracture-injection tests (DFITs), the superposition-time derivative has an upward deflection that does not represent actual reservoir or transient behavior. I review mathematical properties of the superposition-time derivative. I derive equations for the pressure transient in a simplified model DFIT in which closure does not occur. I show that the onset of late-time impulse flow is controlled by injection volume and formation, wellbore, and fracture properties, not the duration of injection (as implied by the definition of superposition time). Log-log superposition-time derivative plots of DFITs exhibit a slope of 3/2 at intermediate time. However, pressure change never scales with a 3/2 power of time. One form of the G-function superficially resembles a superposition-time function constructed by summing constant-rate solutions with 3/2 power scaling. However, this is not a mathematically or physically valid interpretation. The 3/2 power arises from a spatial integration of the Carter leakoff solution. There is not a mathematical, physical, or practical justification for plotting DFIT pressure-time data in a way that creates a 3/2 slope. I conclude by providing a field example and practical recommendations for DFIT interpretation.
Abstract Success of the unconventional multi-fractured horizontal well revolution depends on creation of a Stimulated Reservoir Volume (SRV). Advances in stimulation technology have been geared towards creating increasingly larger SRV's. However, the techniques for evaluating the size and shape of the SRV from production data analysis have not kept pace, and need to be improved. In this paper, we review the diagnostic methods that are currently used, and share learnings obtained from analyzing hundreds of unconventional wells from different unconventional plays. We describe the existing specialized analyses, namely plots utilizing square-root of time (and other time functions), along with type curves that were developed for Compound Linear Flow. We demonstrate that even though these type curves do not account for SRV, they can still be used partially to learn about the SRV characteristics. We have studied the behavior of the EFR (Enhanced Frac Region) model and show how it deviates from the Compound Linear Flow type curves. We demonstrate that what is often considered to be linear flow is only a transition between two flow regimes and results in misinterpretation of the linear flow parameters, and consequently, of SRV properties. We have developed a new EFR type curve that helps characterize the SRV. It should provide a better understanding and interpretation of the currently accepted multi-fractured horizontal well/reservoir system, and improve the diagnostic analysis that precedes and reinforces modeling.