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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.
This paper discusses application of superposition to pressure-transient analysis when rate varies significantly before and pressure-transient analysis when rate varies significantly before and during pressure measurements. To apply rigorous superposition, use of conventional pressure-transient and rate-time methods is recommended to estimate permeability, skin, and in some cases, drainage area. These properties allow calculation of the dimensionless time constant used in properties allow calculation of the dimensionless time constant used in superposition calculations on the basis of rate change and dimensionless pressure. As van Everdingen and Meyer proposed, the time constant is varied until a linear fit of the pressure variable is made vs. superposition time. An important step is to use all available rate data, even though pressures may not be measured during periods of rate change. Our work shows the use of full superposition to check the consistency of standard well-test analysis based on the constant-rate or constant-pressure assumption. Data from two gas wells and results from a gas-well simulator provide the basis for our discussion. Problems covered are choosing provide the basis for our discussion. Problems covered are choosing the dimensionless pressure solution, estimating initial pressure by extrapolation of the superposition plot, and analyzing rate-dependent effects.
Well-test analysis based on rate and pressure data is an important tool to the petroleum engineer. It allows estimation of such reservoir properties as permeability, skin, initial or average pressure, and drainage area. Many methods aid the analysis of rate and pressure data, perhaps the most important being the Horner plot for pressure data, perhaps the most important being the Horner plot for buildup analysis, type-curve matching for drawdown and buildup analysis, and the square-root-of-time plot for vertically fractured wells. The results of these analyses are used to determine the need for well treatment, to forecast production, to estimate reserves, and to define well properties for reservoir simulation.
Most well-testing methods use only part of the available pressure and rate data to determine reservoir properties. They often pressure and rate data to determine reservoir properties. They often are based on the constant-rate or constant-flowing-pressure assumption, neither of which is the case for typical oil and gas wells. Well tests may contain several periods of variable rate and shut-in. A given method (e.g., Horner analysis) commonly is applied separately to each buildup period during a multirate test. The permeability and skin from each analysis may be (and usually are) different, leaving the engineer with the problem of assigning an average set of properties to the well.
Several methods use variable-rate data from well tests and production history. The Odeh-Jones method applies superposition production history. The Odeh-Jones method applies superposition with the logarithmic approximation to analyze variable-rate drawdown tests. A limitation of this method is that buildup data with zero rate cannot be analyzed readily with drawdown data. Ridley suggests a unified method based on superposition to analyze drawdown and buildup data simultaneously that also uses log approximation. Fetkovich and Vienot modify the Odeh-Jones method to include the PD function instead of the log approximation. This improvement appears to be useful, particularly in analysis of low permeability, stimulated wells.
Bostic et al. proposed another superposition-based method to calculate a "unit function." This approach also was suggested by van Everdingen and Hurst (among others) for the study of aquifers and by Jargon and van Poollen for variable-rate, variable-pressure well tests.
Abstract The pressure build-up equation derived by Horner is applicable to wells that produce at a constant rate. However, as a constant flow rate does not exist in practice, the Horner equation is not expected to yield accurate results. Because of this limitation, an alternative method must be used to account for a variable production-rate history. The principle of superposition enables the generation of pressure behavior solutions for variable-rate cases based on the constant-rate pressure behavior solutions. The superposition solution and its application in pressure build-up analysis are herein presented and are compared with the Horner method for different interpretation cases. Finally, the accuracy and reliability of the calculated results are discussed.
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.