scholarly journals Deconvolution of Variable-Rate Reservoir Performance Data Using B-Splines

2006 ◽  
Vol 9 (05) ◽  
pp. 582-595 ◽  
Author(s):  
Dilhan Ilk ◽  
Peter P. Valko ◽  
Thomas A. Blasingame

Summary We use B-splines for representing the derivative of the unknown unit-rate drawdown pressure and numerical inversion of the Laplace transform to formulate a new deconvolution algorithm. When significant errors and inconsistencies are present in the data functions, direct and indirect regularization methods are incorporated. We provide examples of under- and over-regularization, and we discuss procedures for ensuring proper regularization. We validate our method using synthetic examples generated without and with errors (up to 10%). Upon validation, we then demonstrate our deconvolution method using a variety of field cases, including traditional well tests, permanent downhole gauge data, and production data. Our work suggests that the new deconvolution method has broad applicability in variable rate/pressure problems and can be implemented in typical well-test and production-data-analysis applications. Introduction The constant-rate drawdown pressure behavior of a well/reservoir system is the primary signature used to classify/establish the characteristic reservoir model. Transient-well-test procedures typically are designed to create a pair of controlled flow periods (a pressure-drawdown/-buildup sequence) and to convert the last part of the response (the pressure buildup) to an equivalent constant-rate drawdown by means of special time transforms. However, the presence of wellbore storage, previous flow history, and rate variations may mask or distort characteristic features in the pressure and rate responses. With the ever-increasing ability to observe downhole rates, it has long been recognized that variable-rate deconvolution should be a viable option to traditional well-testing methods because deconvolution can provide an equivalent constant-rate response for the entire time span of observation. This potential advantage of variable-rate deconvolution has become particularly obvious with the appearance of permanent downhole instrumentation. First and foremost, variable-rate deconvolution is mathematically ill-conditioned; while numerous methods have been developed and applied to deconvolve "ideal" data, very few deconvolution methods perform well in practice. The ill-conditioned nature of the deconvolution problem means that small changes in the input data cause large variations in the deconvolved constant-rate pressures. Mathematically, we are attempting to solve a first-kind Volterra equation [see Lamm (2000)] that is ill-posed. However, in our case the kernel of the Volterra-type equation is the flow-rate function (i.e., the generating function); this function is not known analytically but, rather, is approximated from the observed flow rates. In practical terms, this issue adds to the complexity of the problem (Stewart et al. 1983). In the literature related to variable-rate deconvolution, we find the development of two basic concepts. One concept is to incorporate an a priori knowledge regarding the properties of the deconvolved constant-rate response. The observations of Coats et al. (1964) on the strict monotonicity of the solution led Kuchuk et al. (1990) to impose a "nonpositive second derivative" constraint on pressure response. In some respects, this tradition is maintained in the work given by von Schroeter et al. (2004), Levitan (2003), and Gringarten et al. (2003) when they incorporate non-negativity in the "encoding of the solution." We note that in the examples given, this concept (non-negativity/monotonicity of the solution) requires less-straightforward numerical methods (e.g., nonlinear least-squares minimization). The second concept is to use a certain level of regularization (von Schroeter et al. 2004; Levitan 2003; Gringarten et al. 2003), where "regularization" is defined as the act or process of making a system regular or standard (smoothing or eliminating nonstandard or irregular response features). Regularization can be performed indirectly, by representing the desired solution with a restricted number of "elements," or directly, by penalizing the nonsmoothness of the solution. In either case, the additional degree of freedom (the regularization parameter) has to be established, where this is facilitated by the discrepancy principle (effectively tuning the regularization parameter to a maximum value while not causing intolerable deviation between the model and the observations). In some fashion, each deconvolution algorithm developed to date combines these two concepts (non-negativity/monotonicity of the solution or regularization).

2005 ◽  
Vol 8 (02) ◽  
pp. 113-121 ◽  
Author(s):  
Michael M. Levitan

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.


SPE Journal ◽  
2006 ◽  
Vol 11 (01) ◽  
pp. 35-47 ◽  
Author(s):  
Michael M. Levitan ◽  
Gary E. Crawford ◽  
Andrew Hardwick

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.


1981 ◽  
Vol 21 (01) ◽  
pp. 105-114 ◽  
Author(s):  
C.A. Ehlig-Economides ◽  
H.J. Ramey

Abstract Conventional well test analysis has been developed primarily for production at a constant flow rate. However, there are several common reservoir production conditions which result in flow at a constant pressure instead of a constant rate. In the field, wells are produced at constant pressure when fluids flow into a constant-pressure separator and during the rate decline period of reservoir depletion. In geothermal reservoirs, produced fluids may drive a backpressured turbine. Open wells, including artesian water wells, flow at constant atmospheric pressure.Most of the existing methods for pressure buildup analysis of wells with a constant-pressure flow history are empirical. Few are based on sound theory. Hence, there is a need for a thorough treatment of pressure buildup behavior following constant-pressure production.In this work, the method of superposition of continuously changing rates was used to generate an exact solution for pressure buildup following constant-pressure flow. The method is general. Storage and skin effects were incorporated into the theory, and both bounded and unbounded reservoirs were considered. Buildup solutions were graphed using conventional techniques for analysis. Horner's method for plotting buildup data after a variable-rate flow was found to be accurate in a majority of cases. Also, the method by Matthews et al. for determining the average reservoir pressure in a closed system was determined to be correct for buildup following constant-pressure flow. Introduction When a flowing well is shut in, the pressure in the wellbore increases with time as the pressures throughout the reservoir approach a static value. Analysis of the pressure increase, or pressure buildup, often provides useful information about the reservoir and the wellbore itself. Techniques exist for determination of wellbore storage, skin effect, reservoir permeability and porosity, and either the initial reservoir pressure or the volumetric average reservoir pressure at the time the well was shut in. Effects of fractures penetrated by or near the wellbore also can be detected, as well as nearby faults or reservoir drainage boundaries.Most of the techniques for pressure buildup analysis were developed for wells which, prior to shut-in, were produced at a constant rate. When the production rate before shut-in changes rapidly, conventional analysis is often suspect. If the exact rate history is known, the theory of superposition in time of constant-rate solution leads to the method derived by Horner which compensates for changing production rates. This method results in long calculations. However, in the same paper Horner proposed a simplified procedure in which the last established rate was assumed constant and the flow time was set equal to the cumulative production divided by the last established rate. Other methods for analysis of pressure buildup after a variable-rate production history were proposed by Odeh et al.A special case of variable-rate production results when a well is produced at constant pressure. The first published application of pressure buildup analysis for a well produced at constant pressure prior to shut-in was by Jacob and Lohman. Their graph of residual drawdown vs. total time divided by shut-in time results in a semilog straight line. SPEJ P. 105^


2011 ◽  
Vol 383-390 ◽  
pp. 243-247
Author(s):  
Ying Hao Shen ◽  
Shun Li He ◽  
Hong Ling Zhang

Pressure-rate deconvolution method based on the newly robust solution algorithm is applied to low permeability reservoirs, and deconvolution codes were developed for the study based on Schreoter deconvolution algorithm in this paper. The application of this method in a low permeability oilfield shows that deconvolution can provide much more information than the conventional well test interpretation methods, and this deconvolution method can interpret the whole test sequence but doesn’t be limited in pressure build-up period. It is proved that the pressure-rate deconvolution algorithm works well in well test interpretation of low permeability reservoirs.


2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Yueming Cheng ◽  
W. John Lee ◽  
Duane A. McVay

Deconvolution allows the test analyst to estimate the constant-rate transient pressure response of a reservoir-well system, and assists us in system identification and parameter estimation. Unfortunately, deconvolution amplifies the noise contained in data. Often, we cannot identify the reservoir system from deconvolved results owing to solution instability caused by noise in measured data. We previously presented a deconvolution technique based on the fast Fourier transform that we applied to a single buildup or drawdown period. In this paper, we extend our previous work and apply the deconvolution technique based on the fast Fourier transform to arbitrarily changing rate profiles such as multirate tests. The deconvolution results, which represent a constant-rate pressure drawdown response spanning the entire duration of the test, can provide helpful insight into the correct reservoir description. We have improved our original deconvolution method in number of ways, particularly with the introduction of an iterative algorithm that produces stable deconvolution results. We demonstrate application of our deconvolution method to analysis of synthetic and field examples, including both flow and shut-in periods. Our deconvolution method can efficiently reproduce the characteristic responses of the reservoir-well system and increase our confidence in parameter estimates.


SPE Journal ◽  
2008 ◽  
Vol 13 (02) ◽  
pp. 226-247 ◽  
Author(s):  
Mustafa Onur ◽  
Murat Cinar ◽  
Dilhan Ilk ◽  
Peter P. Valko ◽  
Thomas A. Blasingame ◽  
...  

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.


2021 ◽  
Author(s):  
Gabriela Chaves ◽  
Danielle Monteiro ◽  
Virgilio José Martins Ferreira

Abstract Commingle production nodes are standard practice in the industry to combine multiple segments into one. This practice is adopted at the subsurface or surface to reduce costs, elements (e.g. pipes), and space. However, it leads to one problem: determine the rates of the single elements. This problem is recurrently solved in the platform scenario using the back allocation approach, where the total platform flowrate is used to obtain the individual wells’ flowrates. The wells’ flowrates are crucial to monitor, manage and make operational decisions in order to optimize field production. This work combined outflow (well and flowline) simulation, reservoir inflow, algorithms, and an optimization problem to calculate the wells’ flowrates and give a status about the current well state. Wells stated as unsuited indicates either the input data, the well model, or the well is behaving not as expected. The well status is valuable operational information that can be interpreted, for instance, to indicate the need for a new well testing, or as reliability rate for simulations run. The well flowrates are calculated considering three scenarios the probable, minimum and maximum. Real-time data is used as input data and production well test is used to tune and update well model and parameters routinely. The methodology was applied using a representative offshore oil field with 14 producing wells for two-years production time. The back allocation methodology showed robustness in all cases, labeling the wells properly, calculating the flowrates, and honoring the platform flowrate.


2021 ◽  
Author(s):  
Nagaraju Reddicharla ◽  
Subba Ramarao Rachapudi ◽  
Indra Utama ◽  
Furqan Ahmed Khan ◽  
Prabhker Reddy Vanam ◽  
...  

Abstract Well testing is one of the vital process as part of reservoir performance monitoring. As field matures with increase in number of well stock, testing becomes tedious job in terms of resources (MPFM and test separators) and this affect the production quota delivery. In addition, the test data validation and approval follow a business process that needs up to 10 days before to accept or reject the well tests. The volume of well tests conducted were almost 10,000 and out of them around 10 To 15 % of tests were rejected statistically per year. The objective of the paper is to develop a methodology to reduce well test rejections and timely raising the flag for operator intervention to recommence the well test. This case study was applied in a mature field, which is producing for 40 years that has good volume of historical well test data is available. This paper discusses the development of a data driven Well test data analyzer and Optimizer supported by artificial intelligence (AI) for wells being tested using MPFM in two staged approach. The motivating idea is to ingest historical, real-time data, well model performance curve and prescribe the quality of the well test data to provide flag to operator on real time. The ML prediction results helps testing operations and can reduce the test acceptance turnaround timing drastically from 10 days to hours. In Second layer, an unsupervised model with historical data is helping to identify the parameters that affecting for rejection of the well test example duration of testing, choke size, GOR etc. The outcome from the modeling will be incorporated in updating the well test procedure and testing Philosophy. This approach is being under evaluation stage in one of the asset in ADNOC Onshore. The results are expected to be reducing the well test rejection by at least 5 % that further optimize the resources required and improve the back allocation process. Furthermore, real time flagging of the test Quality will help in reduction of validation cycle from 10 days hours to improve the well testing cycle process. This methodology improves integrated reservoir management compliance of well testing requirements in asset where resources are limited. This methodology is envisioned to be integrated with full field digital oil field Implementation. This is a novel approach to apply machine learning and artificial intelligence application to well testing. It maximizes the utilization of real-time data for creating advisory system that improve test data quality monitoring and timely decision-making to reduce the well test rejection.


Sign in / Sign up

Export Citation Format

Share Document