SUMMARYFor the numerical inversion of Laplace transforms we suggest to use multi-precision computing with the level of precision determined by the algorithm. We present two such procedures. The GaverWynn-Rho (GWR) algorithm is based on a special sequence acceleration of the Gaver functionals and requires the evaluation of the transform only on the real line. The fixed Talbot (FT) method is based on the deformation of the contour of the Bromwich inversion integral and requires complex arithmetic. Both GWR and FT have only one free parameter: M, which is the number of terms in the summation. Both algorithms provide increasing accuracy as M increases and can be realized in a few lines using current Computer Algebra Systems.

An eigenvalue-eigenvector analysis is used to extract meaningful kinetic information from linear sensitivity coefficients computed for several species of a reacting system at several time points. The main advantage of this method lies in its ability to reveal those parts of the mechanism which consist of strongly interacting reactions, and to indicate their importance within the mechanism. Results can be used to solve three general kinetic problems. Firstly, an objective condition for constructing a minimal reaction set is presented. Secondly, the uncovered dependencies among the parameters are shown to confirm or deny validity of quasi-steady-state assumptions under the considered experimental conditions. Thirdly, taking into account only sensitivities of observed species, the analysis is used to yield error estimates on unknown parameters determined from the experimental observations, and to suggest the parameters that should be kept fixed in the estimation procedure. To illustrate we chose the well-known hydrogen-bromine reaction and the kinetics of formaldehyde oxidation in the presence of co.

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This work combines two ideas—the stretched exponential decline curve model and the novel paradigm of data-intensive discovery—to provide a controlled production forecast for any individual tight gas/shale gas well on the basis of data gathered through parameter processing for a large group of wells.. Group production for a large number of wells follows stretched exponential decline behavior of production rates, which we model using the corresponding decline curve model. Compared to the Arps model, the new approach offers numerous advantages; the two most significant ones are the bounded nature of estimated ultimate recovery (EUR) without limits on time or rate, and the straight-line behavior of a recovery potential expression that we introduce. This approach moves production forecasts in tight and unconventional gas fields from individual and subjective curve matching to a new methodology we call "group-data controlled forecast." In terms of the novel stretched exponential decline curve model, the combined process offers statistically more consistent reserve estimates and also provides a potential well monitoring tool.

Analysis of publicly available monthly production history and well completion records can shed light onto such long-standing questions as 1) what is the value of a stimulation (re-stimulation) treatment in the Barnett Shale, 2) how does the ultimate recovery depend on treatment type and size, 3) what factors determine the performance of a fractured well. This study starts with the month-by-moth analysis of production history for all gas wells in the Barnett Shale. Using a specialized decline-curve analysis methodology developed for shale gas wells, significant production behavior changes are automatically detected and jumps in estimated ultimate recoveries are calculated for individual wells as well, as for groups of wells. The study then continues with the textual analysis of publicly available well completion records consisting of more than 16 Gigabyte data. The obtained database is submitted to analysis relating ultimate recovery to well inclination, to location, to treatment parameters, etc. Introduction Gas shales consist of fine-grained sedimentary rocks (shale to siltstone) containing a minimum of 0.5 weight percent total organic carbon. The amount, type, and thermal maturity of this organic matter determine the type and quantity of hydrocarbons in-place. Gas shales may contain biogenic to thermogenic methane that can be either sorbed on organic matter or occurring as free gas in the pores and naturally existing fractures (Cardott 2006). Shale gas reservoirs are self-sourcing where migration has been limited. The first large-scale, commercially successful shale gas development has been the Barnett Shale in the Fort Worth Basin. There is a vast literature on the geophysical and petrophysical characteristics of the Barnett Shale (see for instance Bowker 2007, Gale, Reed and Holder J. 2007, Jacobi et al. 2008, Matthews, Schein and Malone 2007, Walser and Pursell 2008, Zhao, Givens and Curtis 2007.) The petroleum engineering literature is abundant on studies regarding completion techniques in the area (Lancaster et al. 1992, Coulter, Benton and Thomson 2004, Coulter et al. 2006, Ketter et al. 2006, Moore and Ramakrishnan 2006, Jennings et al. 2007, Zahid et al. 2007, Economides and Martin 2007, Miskimins, J.L. 2008, Shelley et al. 2008) and on assessing fracture geometry (Fisher et al. 2002, Fisher et al. 2004, Siebrits et al. 2000, Steinsberger 2005, Suarez-Rivera et al. 2006, Mayerhofer et al. 2006.) Reserve estimates are discussed in detail by Montgomery et al. 2005, Pollastro 2007 and Pollastro et al. 2007. At the writing of this paper (October, 2008), according to the HPDI database there are 10,690 gas wells in the field that have been produced for at least one month. (Notice the change from 7,000 to 10,000 in the short time interval between the paper proposal was accepted and the actual paper was prepared.) Figure 1 shows the study area, its subdivision into 5 miles by 5 miles subareas, the location of city centers and the location of the wellheads. The ability to analyze production histories of more than ten thousand gas wells concentrated both in location and time is an unprecedented opportunity but requires a specialized approach. We have developed a new decline curve model and data processing procedure for this purpose.

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This 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. iv 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.

Conventional multiple regression for permeability estimation from well logs requires a functional relationship to be presumed. Because of the inexact nature of the relationship between petrophysical variables, it is not always possible to identify the underlying functional form between dependent and independent variables in advance. When large variations in petrological properties are exhibited, parametric regression often fails or leads to unstable and erroneous results, especially for multivariate cases.In this paper, we describe a nonparametric approach for estimating optimal transformations of petrophysical data to obtain the maximum correlation between observed variables. The approach does not require a priori assumptions of a functional form, and the optimal transformations are derived solely based on the data set. Unlike neural networks, such transformations can facilitate physically based function identification. An iterative procedure involving the alternating conditional expectation (ACE) forms the basis of our approach. The power of ACE is illustrated using synthetic as well as field examples. The results clearly demonstrate improved permeability estimation by ACE compared to conventional parametric-regression methods.