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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.
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 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.
Summary. A reliable estimate of the formation parting or fracture extension pressure is important for efficient operation of waterfloods and tertiary recovery projects. A new procedure, called a two-step rate test procedure, called a two-step rate test (2-SRT), is presented for determining this pressure. Unlike a conventional step rate test (SRT), which consists of several constant-rate injection steps, the 2-SRT requires only two injection steps, during which pressures are measured continuously. Test procedure, design and analysis procedure, design and analysis considerations, and recommendations for test implementation are provided. Field examples are included. The 2-SRT procedure offers potential for time procedure offers potential for time and cost savings over a conventional SRT.
Rapid water breakthrough in production wells as a direct result of exceeding a certain critical injection pressure in nearby injection wells was observed as early as 1945. This critical injection pressure is called the formation or fracture parting pressure (FPP). The FPP is equivalent to the "fracture extension/propagation pressure" in the hydraulic fracturing literature. Several studies recently demonstrated that a fracture will continue to propagate if injection is above the FPP and the injection/ withdrawal ratio is greater than one. In addition to this uncontrolled fracture extension, injection above the FPP may also cause fracturing out of pay. These factors may lead to premature breakthrough of injected fluids, poor sweep efficiency, reduced recovery, poor sweep efficiency, reduced recovery, and loss of costly injection fluids. On the other hand, injection far below the FPP may result in injection volumes much lower than the allowable maximum and a reduced rate of oil recovery. A reliable estimate of the FPP is therefore critical in conducting secondary and tertiary recovery projects. The SRT has been the primary method used for several years to determine FPP. A recent paper provided a detailed discussion of the design and analysis of SRT'S. To define the FPP adequately from an SRT, several (usually seven or more) constant-rate injection steps, generally of equal duration, are needed. Further, the duration of each step (also referred to as timestep size) should ideally be long enough for the data to be free of wellbore-storage effects. If continuous pressure measurements are available during pressure measurements are available during an SRT, the data can be analyzed by multiple-rate superposition methods to determine the FPP. The Odeh and Jones superposition method or Agarwal's multirate equivalent time analysis can be used to analyze SRT data. Ref. 7 gives a detailed discussion of the proper application of multiple-rate analysis and identification of FPP from such an analysis.
This paper describes a new test procedure (2-SRT) for determining FPP. The 2-SRT requires only two constant-rate steps, during which pressure and time data are measured continuously and analyzed for determination of the FPP by multiple-rate superposition methods. Pressure data from the two steps are compared on Agarwal's multiple-rate equivalent-time basis. Guidelines for the design and analysis of a 2-SRT and recommendations regarding the test implementation are provided. Field examples are included to demonstrate the applicability of this procedure. procedure. Discussion
Test Procedure. The 2-SRT can be run in at least four different modes shown schematically in Fig. 1. For each mode, the test well is either shut in or stabilized at a constant injection rate before the start of the test. In either case, the stabilized pressure before the 2-SRT must be below the FPP. Modes 1 through 3 refer to cases where the well is stabilized at a constant injection rate before the test is run. Mode 4 is the case when the well is shut in at the time of the test. The 2-SRT procedure for each mode is described below.
Mode 1. The injection well is shut in for Step 1, followed by injection at a high constant rate for Step 2. The injection rate for Step 2 is chosen such that the FPP will be exceeded.
Mode 2. If the well is on a stabilized low-rate injection, Step 1 of the test may be stepping up the injection rate to a constant value that is still low enough so that the FPP is not exceeded. The injection rate is then further increased to a higher constant rate for Step 2.
Mode 3. The injection is reduced to a lower constant rate for Step 1 and then increased to a higher constant rate for Step 2.
Mode 4. The well is stabilized at shut-in conditions. The 2-SRT consists of two constant-rate injection steps with a stepwise increase in the injection rate for each step.
For all the modes of the 2-SRT procedure, it is extremely important that the pressures attained for the entire duration of Step 1 are below the FPP. The injection rate for Step 2 is chosen such that the injection pressure will exceed the FPP during this step.