Practical Application of Pressure-Rate Deconvolution to Analysis of Real Well Tests

2005 ◽  
Vol 8 (02) ◽  
pp. 113-121 ◽  
Author(s):  
Michael M. Levitan
Keyword(s):  
Test Data ◽  
Rate Data ◽  
Well Test ◽  
Pressure Data ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Deconvolution Algorithm ◽  
Constant Rate ◽  
Test Pressure ◽  
Real Test

Summary Pressure/rate deconvolution is a long-standing problem of well-test analysis that has been the subject of research by a number of authors. A variety of different deconvolution algorithms have been proposed in the literature. However, none of them is robust enough to be implemented in the commercial well-test-analysis software used most widely in the industry. Recently, vonSchroeter et al.1,2 published a deconvolution algorithm that has been shown to work even when a reasonable level of noise is present in the test pressure and rate data. In our independent evaluation of the algorithm, we have found that it works well on consistent sets of pressure and rate data. It fails, however, when used with inconsistent data. Some degree of inconsistency is normally present in real test data. In this paper, we describe the enhancements of the deconvolution algorithm that allow it to be used reliably with real test data. We demonstrate the application of pressure/rate deconvolution analysis to several real test examples. Introduction The well bottomhole-pressure behavior in response to a constant-rate flow test is a characteristic response function of the reservoir/well system. The constant-rate pressure-transient response depends on such reservoir and well properties as permeability, large-scale reservoir heterogeneities, and well damage (skin factor). It also depends on the reservoir flow geometry defined by the geometry of well completion and by reservoir boundaries. Hence, these reservoir and well characteristics are reflected in the system's constant-rate drawdown pressure-transient response, and some of these reservoir and well characteristics may potentially be recovered from the response function by conventional methods of well-test analysis. Direct measurement of constant-rate transient-pressure response does not normally yield good-quality data because of our inability to accurately control rates and because the well pressure is very sensitive to rate variations. For this reason, typical well tests are not single-rate, but variable-rate, tests. A well-test sequence normally includes several flow periods. During one or more of these flow periods, the well is shut in. Often, only the pressure data acquired during shut-in periods have the quality required for pressure-transient analysis. The pressure behavior during the individual flow period of a multirate test sequence depends on the flow history before this flow period. Hence, it is not the same as a constant-rate system-response function. The well-test-analysis theory that evolved over the past 50 years has been built around the idea of applying a special time transform to the test pressure data so that the pressure behavior during individual flow periods would be similar in some way to constant-rate drawdown-pressure behavior. The superposition-time transform commonly used for this purpose does not completely remove all effects of previous rate variation. There are sometimes residual superposition effects left, and this often complicates test analysis. An alternative approach is to convert the pressure data acquired during a variable-rate test to equivalent pressure data that would have been obtained if the well flowed at constant rate for the duration of the whole test. This is the pressure/rate deconvolution problem. Pressure/rate deconvolution has been a subject of research by a number of authors over the past 40 years. Pressure/rate deconvolution reduces to the solution of an integral equation. The kernel and the right side of the equation are given by the rate and the pressure data acquired during a test. This problem is ill conditioned, meaning that small changes in input (test pressure and rates) lead to large changes in output result—a deconvolved constant-rate pressure response. The ill-conditioned nature of the pressure/rate deconvolution problem, combined with errors always present in the test rate and pressure data, makes the problem highly unstable. A variety of different deconvolution algorithms have been proposed in the literature.3–8 However, none of them is robust enough to be implemented in the commercial well-test-analysis software used most widely in the industry. Recently, von Schroeter et al.1,2 published a deconvolution algorithm that has been shown to work when a reasonable level of noise is present in test pressure and rate data. In our independent implementation and evaluation of the algorithm, we have found that it works well on consistent sets of pressure and rate data. It fails, however, when used with inconsistent data. Examples of such inconsistencies include wellbore storage or skin factor changing during a well-test sequence. Some degree of inconsistency is almost always present in real test data. Therefore, the deconvolution algorithm in the form described in the references cited cannot work reliably with real test data. In this paper, we describe the enhancements of the deconvolution algorithm that allow it to be used reliably with real test data. We demonstrate application of the pressure/rate deconvolution analysis to several real test examples.

Deconvolution of Multiwell Test Data

SPE Journal ◽  
2007 ◽  
Vol 12 (04) ◽  
pp. 420-428 ◽  
Author(s):  
Michael M. Levitan
Keyword(s):  
Test Data ◽  
Rate Variation ◽  
Rate Data ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Deconvolution Analysis ◽  
Deconvolution Algorithm ◽  
Analysis Technique ◽  
Well Tests

Summary The deconvolution analysis technique that evolved with development of the deconvolution algorithms by von Schroeter et al. (2004), Levitan (2005), and Levitan et al. (2006) became a useful addition to the suite of techniques used in well-test analysis. This deconvolution algorithm, however, is limited to the pressure and rate data that originate from a single active well on the structure. It is ideally suited for analysis of the data from exploration and appraisal well tests. The previously mentioned deconvolution algorithm can not be used with the data that are acquired during startup and early field development that normally involve several producing wells. The paper describes a generalization of deconvolution to multiwell pressure and rate data. Several approaches and ideas for multiwell deconvolution are investigated and evaluated. The paper presents the results of this investigation and demonstrates performance of the deconvolution algorithm on synthetic multiwell test data. Introduction Pressure-rate deconvolution is a way of reconstructing the characteristic pressure transient behavior of a reservoir-well system hidden in the test data by well-rate variation during a test. The deconvolution analysis technique that evolved with development of the deconvolution algorithms by von Schroeter et al. (2004), Levitan (2005), and Levitan et al. (2006) became a useful addition to the suite of techniques used in well-test analysis. It has been implemented in commercial well-test analysis software and is routinely used for analysis of well tests. This deconvolution algorithm, however, is applicable only for the case when there is just one active well in the reservoir. It is ideally suited for analysis of exploration and appraisal well tests. The previously described deconvolution algorithm cannot be used for well-test analysis when there are several active wells operating in the field and the bottomhole pressure measured in one well during a well test is affected by the production from other wells operating in the same reservoir. The deconvolution algorithm has to be generalized so that it is possible to remove not only the effects of rate variation of the well itself but also the pressure interferences with other wells in the reservoir. As a result, we would be able to reconstruct the true characteristic well-pressure responses to unit-rate production of each producing well in the reservoir. These responses reflect the reservoir and well properties and could be used for recovering these properties by the techniques of pressure-transient analysis. Multiwell deconvolution thus becomes in a way a general technique for interference well-test analysis. The problem, however, is that the interference pressure signals produced by other wells are small compared to the pressure signal caused by the production of the well itself. These pressure interference signals are delayed in time and the time delay depends on the distance between respective wells. All this makes multiwell deconvolution an extremely difficult problem.

An Investigation of Recent Deconvolution Methods for Well-Test Data Analysis

SPE Journal ◽  
2008 ◽  
Vol 13 (02) ◽  
pp. 226-247 ◽  
Author(s):  
Mustafa Onur ◽  
Murat Cinar ◽  
Dilhan Ilk ◽  
Peter P. Valko ◽  
Thomas A. Blasingame ◽  
...  
Keyword(s):  
Data Analysis ◽  
Test Data ◽  
System Response ◽  
Production Data ◽  
Data Sets ◽  
Rate Data ◽  
Well Test ◽  
Rate System ◽  
Constant Rate ◽  
Test Pressure

Summary In this work, we present an investigation of recent deconvolution methods proposed by von Schroeter et al. (2002, 2004), Levitan (2005) and Levitan et al. (2006), and Ilk et al. (2006a, b). These works offer new solution methods to the long-standing deconvolution problem and make deconvolution a viable tool for well-test and production-data analysis. However, there exists no study presenting an independent assessment of all these methods, revealing and discussing specific features associated with the use of each method in a unified manner. The algorithms used in this study for evaluating the von Schroeter et al. and Levitan methods represent our independent implementations of their methods based on the material presented in their papers, not the original algorithms implemented by von Schroeter et al. and Levitan. Three synthetic cases and one field case are considered for the investigation. Our results identify the key issues regarding the successful and practical application of each method. In addition, we show that with proper care and attention in applying these methods, deconvolution can be an important tool for the analysis and interpretation of variable rate/pressure reservoir performance data. Introduction Applying deconvolution for well-test and production data analysis is important because it provides the equivalent constant rate/pressure response of the well/reservoir system affected by variable rates/pressures (von Schroeter et al. 2002, 2004; Levitan 2005; Levitan et al. 2006; Ilk et al. 2006a, b; Kuchuk et al. 2005). With the implementation of permanent pressure and flow-rate measurement systems, the importance of deconvolution has increased because it is now possible to process the well test/production data simultaneously and obtain the underlying well/reservoir model (in the form of a constant rate pressure response). New methods of analyzing well-test data in the form of a constant-rate drawdown system response and production data in the form of a constant-pressure rate system response have emerged with development of robust pressure/rate (von Schroeter et al. 2002, 2004; Levitan 2005; Levitan et al. 2006; Ilk et al. 2006a, b) and rate/pressure (Kuchuk et al. 2005) deconvolution algorithms. In this work, we focus on the pressure/rate deconvolution for analyzing well-test data. For over a half century, pressure/rate deconvolution techniques have been applied to well-test pressure and rate data as a means to obtain the constant-rate behavior of the system (Hutchinson and Sikora 1959; Coats et al. 1964; Jargon and van Poollen 1965; Kuchuk et al. 1990; Thompson and Reynolds 1986; Baygun et al. 1997). A thorough review and list of the previous deconvolution algorithms can be found in von Schroeter et al. (2004). The primary objective of applying pressure/rate deconvolution is to convert the pressure data response from a variable-rate test or production sequence into an equivalent pressure profile that would have been obtained if the well were produced at a constant rate for the entire duration of the production history. If such an objective could be achieved with some success, then, as stated by Levitan, the deconvolved response would remove the constraints of conventional analysis techniques (Earlougher 1977; Bourdet 2002) that have been built around the idea of applying a special time transformation [e.g., the logarithmic multirate superposition time (Agarwal 1980)] to the test pressure data so that the pressure behavior observed during individual flow periods would be similar in some way to the constant-rate system response. As also stated by Levitan, the superposition-time transform does not completely remove all effects of previous rate variations and often complicates test analysis because of residual superposition effects. Unfortunately, deconvolution is an ill-posed inverse problem and will usually not have a unique solution even in the absence of noise in the data. Even if the solution is unique, it is quite sensitive to noise in the data, meaning that small changes in input (measured pressure and rate data) can lead to large changes in the output (deconvolved) result. Therefore, this ill-posed nature of the deconvolution problem combined with errors that are inherent in pressure and rate data makes the application of deconvolution a challenge, particularly so in terms of developing robust deconvolution algorithms which are error-tolerant. Although there exists a variety of different deconvolution algorithms proposed in the past, only those developed by von Schroeter et al., Levitan, and Ilk et al. appear to offer the necessary robustness to make deconvolution a viable tool for well-test and production data analysis. In this paper, our objectives are to conduct an investigation of these three deconvolution methods and to establish the advantages and limitations of each method. As stated in the abstract, the algorithms used in this study for evaluating the von Schroeter et al. and Levitan methods represent our independent implementations based on the material presented in their papers; therefore, our implementations may not be identical to their versions. However, as is shown later, validation conducted on the simulated (test) data sets (von Schroeter et al. 2004; Levitan 2005) sent to us directly by von Schroeter and Levitan shows that our implementations reproduce almost exactly the same results generated by their original algorithms for these simulated data sets. The paper is organized as follows: First, we describe the pressure/rate deconvolution model and error model considered in this work. Then, we provide the mathematical background of the von Schroeter et al., Levitan, and Ilk et al. methods together with their specific features. We compare the performance of each method by considering three synthetic and one field well-test data sets. Finally, we provide a discussion of our results obtained from this investigation.

Connecting Data, Model and Process to Streamline and Enhance Single-Point Production Well Test Validation

2021 ◽  
Author(s):  
Mohamad Mustaqim Mokhlis ◽  
Nurdini Alya Hazali ◽  
Muhammad Firdaus Hassan ◽  
Mohd Hafiz Hashim ◽  
Afzan Nizam Jamaludin ◽  
...  
Keyword(s):  
Test Data ◽  
Single Point ◽  
Database Systems ◽  
Test Validation ◽  
Well Test ◽  
Production Well ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Digital Ecosystem ◽  
Well Model

Abstract In this paper we will present a process streamlined for well-test validation that involves data integration between different database systems, incorporated with well models, and how the process can leverage real-time data to present a full scope of well-test analysis to enhance the capability for assessing well-test performance. The workflow process demonstrates an intuitive and effective way for analyzing and validating a production well test via an interactive digital visualization. This approach has elevated the quality and integrity of the well-test data, as well as improved the process cycle efficiency that complements the field surveillance engineers to keep track of well-test compliance guidelines through efficient well-test tracking in the digital interface. The workflow process involves five primary steps, which all are conducted via a digital platform: Well Test Compliance: Planning and executing the well test Data management and integration Well Test Analysis and Validation: Verification of the well test through historical trending, stability period checks, and well model analysis Model validation: Correcting the well test and calibrating the well model before finalizing the validity of the well test Well Test Re-testing: Submitting the rejected well test for retesting and final step Integrating with corporate database system for production allocation This business process brings improvement to the quality of the well test, which subsequently lifts the petroleum engineers’ confidence level to analyze well performance and deliver accurate well-production forecasting. A well-test validation workflow in a digital ecosystem helps to streamline the flow of data and system integration, as well as the way engineers assess and validate well-test data, which results in minimizing errors and increases overall work efficiency.

Practical Considerations for Pressure-Rate Deconvolution of Well Test Data

SPE Journal ◽  
2006 ◽  
Vol 11 (01) ◽  
pp. 35-47 ◽  
Author(s):  
Michael M. Levitan ◽  
Gary E. Crawford ◽  
Andrew Hardwick
Keyword(s):  
Test Data ◽  
Transient Behavior ◽  
Test Sequence ◽  
System Response ◽  
Rate Variation ◽  
Well Test ◽  
Pressure Transient ◽  
Pressure Behavior ◽  
Deconvolution Algorithm ◽  
Constant Rate

Summary Pressure-rate deconvolution provides equivalent representation of variable-rate well-test data in the form of characteristic constant rate drawdown system response. Deconvolution allows one to develop additional insights into pressure transient behavior and extract more information from well-test data than is possible by using conventional analysis methods. In some cases, it is possible to interpret the same test data in terms of larger radius of investigation. There are a number of specific issues of which one has to be aware when using pressure-rate deconvolution. In this paper, we identify and discuss these issues and provide practical considerations and recommendations on how to produce correct deconvolution results. We also demonstrate reliable use of deconvolution on a number of real test examples. Introduction Evaluation and assessment of pressure transient behavior in well-test data normally begins with examination of test data on different analysis plots [e.g., a Bourdet (1983, 1989) derivative plot, a superposition (semilog) plot, or a Cartesian plot]. Each of these plots provides a different view of the pressure transient behavior hidden in the test data by well-rate variation during a test. Integration of these several views into one consistent picture allows one to recognize, understand, and explain the main features of the test transient pressure behavior. Recently, a new method of analyzing test data in the form of constant rate drawdown system response has emerged with development of robust pressure-rate deconvolution algorithm. (von Schroeter et al. 2001, 2004; Levitan 2005). Deconvolved drawdown system response is another way of presenting well-test data. Pressure--rate deconvolution removes the effects of rate variation from the pressure data measured during a well-test sequence and reveals underlying characteristic system behavior that is controlled by reservoir and well properties and is not masked by the specific rate history during the test. In contrast to a Bourdet derivative plot or to a superposition plot, which display the pressure behavior for a specific flow period of a test sequence, deconvolved drawdown response is a representation of transient pressure behavior for a group of flow periods included in deconvolution. As a result, deconvolved system response is defined on a longer time interval and reveals the features of transient behavior that otherwise would not be observed with conventional analysis approach. The deconvolution discussed in this paper is based on the algorithm first described by von Schroeter, Hollaender, and Gringarten (2001, 2004). An independent evaluation of the von Schroeter et al. algorithm by Levitan (2005) confirmed that with some enhancements and safeguards it can be used successfully for analysis of real well-test data. There are several enhancements that distinguish our form of the deconvolution algorithm. The original von Schroeter algorithm reconstructs only the logarithm of log-derivative of the pressure response to constant rate production. Initial reservoir pressure is supposed to be determined in the deconvolution process along with the deconvolved drawdown system response. However, inclusion of the initial pressure in the list of deconvolution parameters often causes the algorithm to fail. For this reason, the authors do not recommend determination of initial pressure in the deconvolution process (von Schroeter et al. 2004). It becomes an input parameter and has to be evaluated through other means. Our form of deconvolution algorithm reconstructs the pressure response to constant rate production along with its log-derivative. Depending on the test sequence, in some cases we can recover the initial reservoir pressure.

scholarly journals A New Method for De-Noising of Well Test Pressure Data Base on Legendre Approximation

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 989
Author(s):  
Fengbo Zhang ◽  
Yuandan Zheng ◽  
Zhenyu Zhao ◽  
Zhi Li
Keyword(s):  
Test Data ◽  
Numerical Approximation ◽  
Convergence Result ◽  
New Method ◽  
Well Test ◽  
Pressure Data ◽  
Numerical Tests ◽  
Test Pressure ◽  
Legendre Expansion ◽  
Derivatives Of

In this paper, noise removing of the well test data is considered. We use the Legendre expansion to approximate well test data and a truncated strategy has been employed to reduce noise. The parameter of the truncation will be chosen by a discrepancy principle and a corresponding convergence result has been obtained. The theoretical analysis shows that a well numerical approximation can be obtained by the new method. Moreover, we can directly obtain the stable numerical derivatives of the pressure data in this method. Finally, we give some numerical tests to show the effectiveness of the method.

Reservoir Characterization Constrained to Well-Test Data: A Field Example

2000 ◽  
Vol 3 (04) ◽  
pp. 325-334 ◽  
Author(s):  
J.L. Landa ◽  
R.N. Horne ◽  
M.M. Kamal ◽  
C.D. Jenkins
Keyword(s):  
Mathematical Model ◽  
Test Data ◽  
Pressure Response ◽  
Well Testing ◽  
Pressure Measurements ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Reservoir Description ◽  
Different Sources

Summary In this paper we present a method to integrate well test, production, shut-in pressure, log, core, and geological data to obtain a reservoir description for the Pagerungan field, offshore Indonesia. The method computes spatial distributions of permeability and porosity and generates a pressure response for comparison to field data. This technique produced a good match with well-test data from three wells and seven shut-in pressures. The permeability and porosity distributions also provide a reasonable explanation of the observed effects of a nearby aquifer on individual wells. As a final step, the method is compared to an alternate technique (object modeling) that models the reservoir as a two-dimensional channel. Introduction The Pagerungan field has been under commercial production since 1994. This field was chosen to test a method of integrating dynamic well data and reservoir description data because the reservoir has only produced single phase gas, one zone in the reservoir is responsible for most of the production, and good quality well-test, core, and log data are available for most wells. The method that was used to perform the inversion of the spatial distribution of permeability and porosity uses a parameter estimation technique that calculates the gradients of the calculated reservoir pressure response with respect to the permeability and porosity in each of the cells of a reservoir simulation grid. The method is a derivative of the gradient simulator1 approach and is described in Appendices A and B. The objective is to find sets of distributions of permeability and porosity such that the calculated response of the reservoir closely matches the pressure measurements. In addition, the distributions of permeability and porosity must satisfy certain constraints given by the geological model and by other information known about the reservoir. Statement of Theory and Definitions The process of obtaining a reservoir description involves using a great amount of data from different sources. It is generally agreed that a reservoir description will be more complete and reliable when it is the outcome of a process that can use the maximum possible number of data from different sources. This is usually referred to in the literature as "data Integration." Reservoir data can be classified as "static" or "dynamic" depending on their connection to the movement or flow of fluids in the reservoir. Data that have originated from geology, logs, core analysis, seismic and geostatistics can be generally classified as static; whereas the information originating from well testing and the production performance of the reservoir can be classified as dynamic. So far, most of the success in data integration has been obtained with static information. Remarkably, it has not yet become common to completely or systematically integrate dynamic data with static data. A number of researchers,2–5 are studying this problem at present. This work represents one step in that direction. Well Testing as a Tool for Reservoir Description. Traditional well-test analysis provides good insight into the average properties of the reservoir in the vicinity of a well. Well testing can also identify the major features of relatively simple reservoirs, such as faults, fractures, double porosity, channels, pinchouts, etc. in the near well area. The difficulties with this approach begin when it is necessary to use the well-test data on a larger scale, such as in the context of obtaining a reservoir description. One of the main reasons for these difficulties is that traditional well-test analysis handles transient pressure data collected at a single well at a time, and is restricted to a small time range. As a result, traditional well-test analysis does not make use of "pressure" events separated in historical time. The use of several single and multiple well tests to describe reservoir heterogeneity has been reported in the literature,6 however, this approach is not applied commonly because of the extensive efforts needed to obtain a reservoir description. The method presented in this paper uses a numerical model of the reservoir to overcome these shortcomings. It will be shown that pressure transients can be used effectively to infer reservoir properties at the scale of reservoir description. Well-test data, both complete tests and occasional spot pressure measurements, will be used to this effect. The well-test information allows us to infer properties close to the wells and, when combined with the shut-in pressures (spot pressure), boundary information and permeability-porosity correlations, provides the larger scale description. General Description of the Method The proposed method is similar to other parameter estimation methods and thus consists of the following major items: the mathematical model, the objective function and the minimization algorithm. Mathematical Model. Because of the complexity of the reservoir description, the reservoir response must be computed numerically. Therefore, the pressure response is found using a numerical simulator. The reservoir is discretized into blocks. The objective is to find a suitable permeability-porosity distribution so that values of these parameters can be assigned to each of the blocks.

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