TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractIn this paper, new explicit analytical equations for stabilized and transient deliverability coefficients in terms of formation/fluid parameters are presented. These equations are derived for fully and partially penetrating vertical wells and for fully penetrating horizontal wells. The proposed equations use the relationship between the empirical (Rawlins and Schellhardt) deliverability equation and rigorous (or Forechheimer's) deliverability equations for both stabilized and unstabilized (transient) flow conditions. Based on these new equations, we also present new methods for determining not only the performance coefficients, but also formation parameters from stabilized and transient gas deliverability data. Unlike the existing methods, our new methods do not require geometric mean of pressure or rate data. This is a distinct advantage of the methods presented in this paper over the existing methods because determination of geometric mean of pressure or rate data may be quite difficult, and the mean value is quite sensitive to the measurement errors in such data. Thus, the methods given in this paper should prove very useful for determining formation parameters accurately from deliverability tests in vertical and horizontal wells. The accuracy and applicability of the methods given in this study are verified by analyzing two test data published previously in the literature. Results are compared with those obtained from the existing methods in the literature and indicate that combination of our new methods with the Hinchman-Kazemi-Poettmann method for isochronal test types provides more information about the formation and reliable deliverability forecasting.

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractIn recent years, it is shown that the inverse problem theory based on Bayesian estimation provides a powerful methodology not only to generate rock property fields conditioned to both static and dynamic data, but also to assess the uncertainty in performance predictions. To date, standard applications of inverse problem theory given in the literature assume that rock property fields obey multinormal distribution and are second order stationary. In this work, we extend the inverse problem theory to cases where rock property fields (only porosity and permeability fields are considered) can be characterized by fractal distributions. Fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) are considered. To the authors' knowledge, there exists no study in the literature considering generation of fractal rock property fields conditioned to dynamic data; particularly to well-test pressure data.We show that available Bayesian estimation techniques based on the assumption of normal/second-order stationary distributions can be directly used to generate conditional fGn rock property fields to both hard and pressure data because fGn distributions are normal/second-order stationary. On the other hand, we show that because fBm is not second-order stationary, these Bayesian estimation techniques can only be used with implementation of a pseudo-covariance (generalized covariance) approach to generate conditional fBm fields to static and well-test pressure data.Using synthetic examples generated from two and threedimensional single-phase flow simulators, we show that the inverse problem methodology can be applied to generate realizations of conditional fBm/fGn porosity and permeability fields to well-test pressure data. We conclude by showing how one can then assess the uncertainty in reservoir performance predictions appropriately using these realizations.