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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.
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 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 Superposition-time functions offer an effective way for handling variable-rate data. However, these functions can also be biased and misleading. The superposition approach may generally be more useful for well-test analysis (constant rate solutions) than rate-transient analysis. Calculated data points do not tend to be sequential with superposition time but do tend to fall on a straight line corresponding to the superposition function chosen. Examples of superposition are logarithm of time (infinite acting vertical wells) and material balance time (boundary dominated flow). Production data from shale gas wells are usually subjected to operating issues that yield noises and outliers. When the rate data are noisy or contain outliers, distinguishing their effects from common regime will be difficult if the superposition time functions are used as a plotting time function on log-log plots. The superposition function may then lead to a log-log plot that has erroneous straight-line segments. A simple technique is presented to rapidly check whether or not there is data bias on the superposition-time specialized plots. The technique is based on evaluating the superposition time function of each flow regime for the maximum production time. Whatever data are beyond the maximum production time (MPT) are considered as biased data and depend on the superposition function chosen. A workflow involving different diagnostic and filtering techniques is proposed. Different synthetic examples and field examples are used in this study. Once all the problematic issues were detected and filtered out, it was clear that superposition time data beyond the MPT is biased and should be ignored. Thus, the proposed MPT technique can be relied on to detect and filter out biased data points on superposition-time log-log plots. Both raw and filtered data were analyzed using type-curve matching of linear-flow typecurves developed by Wattenbarger et al. (1998) for calculating the original gas in place (OGIP). It has been found that biased data yield a noticeable reduction in OGIP. Such reduction is attributed to the early fictitious onset of boundary dominated flow.
This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 149472, "Analyzing Variable-Rate/-Pressure Data in Transient- Linear Flow in Unconventional Gas Reservoirs," by P. Liang, SPE, L. Mattar, SPE, and S. Moghadam, SPE, Fekete Associates, prepared for the 2011 Canadian Unconventional Resources Conference, Calgary, 15-17 November. The paper has not been peer reviewed.
Often, wells in unconventional gas reservoirs exhibit linear flow during their transient period, and this transient behavior can last for several years. Currently, industry uses the type-curve-matching technique to analyze this linear flow. The common type curves assume that wells produce at constant rate. However, the production rate usually is variable and, in fact, is closer to a constant-pressure operation. The constant-pressure type curve is useful, but not suitable when both rate and pressure vary. It is necessary to have an easy-to-use method for analyzing variable-rate/-pressure data in linear flow.
First, the formulation, type curve, specialized graphs, and superposition time used to analyze transient-linear flow for a deeper understanding of the theory are reviewed. Second, a practical and effective method for analyzing variable gas-production data is illustrated. In this development, the effect of skin on the type curve and on the specialized graph was studied. The constant-pressure solution was converted to its constant-rate equivalent by use of material-balance time, and it was found to be acceptable for practical purposes. Real time was converted to corrected pseudotime to account for variable gas properties, and it was determined that the effect would be small in the analysis of actual production data. The effect of outliers on superposition time also was investigated.
The dominant flow regime for wells in most unconventional gas reservoirs is linear flow. The reservoir model in Fig. 1a demonstrates linear flow. A vertical well is drilled in the center of a rectangular reservoir with a biwing hydraulic fracture. The length of the fracture is the same as the width of the reservoir, and the fracture is assumed to have infinite conductivity. These assumptions form the basic reservoir model of linear flow, from which the linear-flow solution was developed. Although this model is simple, it is suitable for analyzing more-complicated reservoir geometries. For example, Fig. 1b represents a cased-hole horizontal well with a number (nf) of equally spaced fractures. All the fractures are assumed to have the same fracture half-length xf. No-flow boundaries (dashed lines in Fig. 1b) form between the fractures. The performance of this system is equal to nf times that of the biwing fracture shown in Fig. 1a.