Browsing by Author "Ilk, Dilhan"
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Item Deconvolution of variable rate reservoir performance data using B-splines(Texas A&M University, 2007-04-25) Ilk, DilhanThis work presents the development, validation and application of a novel deconvolution method based on B-splines for analyzing variable-rate reservoir performance data. Variable-rate deconvolution is a mathematically unstable problem which has been under investigation by many researchers over the last 35 years. While many deconvolution methods have been developed, few of these methods perform well in practice - and the importance of variable-rate deconvolution is increasing due to applications of permanent downhole gauges and large-scale processing/analysis of production data. Under these circumstances, our objective is to create a robust and practical tool which can tolerate reasonable variability and relatively large errors in rate and pressure data without generating instability in the deconvolution process. We propose representing the derivative of unknown unit rate drawdown pressure as a weighted sum of Bsplines (with logarithmically distributed knots). We then apply the convolution theorem in the Laplace domain with the input rate and obtain the sensitivities of the pressure response with respect to individual B-splines after numerical inversion of the Laplace transform. The sensitivity matrix is then used in a regularized least-squares procedure to obtain the unknown coefficients of the B-spline representation of the unit rate response or the well testing pressure derivative function. We have also implemented a physically sound regularization scheme into our deconvolution procedure for handling higher levels of noise and systematic errors. We validate our method with synthetic examples generated with and without errors. The new method can recover the unit rate drawdown pressure response and its derivative to a considerable extent, even when high levels of noise are present in both the rate and pressure observations. We also demonstrate the use of regularization and provide examples of under and over-regularization, and we discuss procedures for ensuring proper regularization. Upon validation, we then demonstrate our deconvolution method using a variety of field cases. Ultimately, the results of our new variable-rate deconvolution technique suggest that this technique has a broad applicability in pressure transient/production data analysis. The goal of this thesis is to demonstrate that the combined approach of B-splines, Laplace domain convolution, least-squares error reduction, and regularization are innovative and robust; therefore, the proposed technique has potential utility in the analysis and interpretation of reservoir performance data.Item Well Performance Analysis for Low to Ultra-low Permeability Reservoir Systems(2010-10-12) Ilk, DilhanUnconventional reservoir systems can best be described as petroleum (oil and/or gas) accumulations which are difficult to be characterized and produced by conventional technologies. In this work we present the development of a systematic procedure to evaluate well performance in unconventional (i.e., low to ultra-low permeability) reservoir systems. The specific tasks achieved in this work include the following: ? Integrated Diagnostics and Analysis of Production Data in Unconventional Reservoirs: We identify the challenges and common pitfalls of production analysis and provide guidelines for the analysis of production data. We provide a comprehensive workflow which consists of model-based production analysis (i.e., rate-transient or model matching approaches) complemented by traditional decline curve analysis to estimate reserves in unconventional reservoirs. In particular, we use analytical solutions (e.g., elliptical flow, horizontal well with multiple fractures solution, etc.) which are applicable to wells produced in unconventional reservoirs. ? Deconvolution: We propose to use deconvolution to identify the correlation between pressure and rate data. For our purposes we modify the B-spline deconvolution algorithm to obtain the constantpressure rate solution using cumulative production and bottomhole pressure data in real time domain. It is shown that constant-pressure rate and constant-rate pressure solutions obtained by deconvolution could identify the correlation between measured rate and pressure data when used in conjunction. ? Series of Rate-Time Relations: We develop three new main rate-time relations and five supplementary rate-time relations which utilize power-law, hyperbolic, stretched exponential, and exponential components to properly model the behavior of a given set of rate-time data. These relations are well-suited for the estimation of ultimate recovery as well as for extrapolating production into the future. While our proposed models can be used for any system, we provide application almost exclusively for wells completed in unconventional reservoirs as a means of providing estimates of time-dependent reserves. We attempt to correlate the rate-time relation model parameters versus model-based production analysis results. As example applications, we present a variety of field examples using production data acquired from tight gas, shale gas reservoir systems.