Decline Curve Analysis of Fractured Reservoirs With Fractal Geometry

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractEvaluation of reservoir parameters through well test and decline curve analysis is a current practice used to estimate formation parameters and to forecast production decline identifying different flow regimes, respectively. From practical experience, it has been observed that certain cases exhibit different wellbore pressure and production behavior from those presented in previous studies. The reason for this difference is not understood completely but it can be found in the distribution of fractures within a Naturally Fractured Reservoir (NFR). Currently, most of these reservoirs are studied by means of Euclidean models, which implicitly assume a uniform distribution of fractures and that all fractures are interconnected.However, evidences from outcrops, well logging, and production behavior studies, and in general, the dynamic behavior observed in these systems, indicate that the above assumptions are not representative for these systems. Thus, the fractal theory can contribute to explain the above.Synthetic and field examples are presented to illustrate the methodology proposed in this work and to demonstrate that the fractal formulation explains consistently the peculiar behavior observed in some real production decline curves.

Pressure responses of a vertically hydraulic fractured well in a reservoir with fractal structure

“…The best known and most useful model to describe the pressure behavior of fractal reservoirs was firstly proposed by Metzler et al [1]. Similarly to Camacho-Velázquez et al [4], from here on we call generalized diffusion equation to the fractal-fractional diffusion (FFD) equation…”

“…The classical diffusion equation has been used to explain the pressure responses of a well in a reservoir, which is assumed to be homogenous at all scales. However, recent studies show that the homogeneity assumption is not valid in most cases [1][2][3][4][5][6][7]. Due to this fact, fractal geometry has been used as an effective tool to describe the heterogeneities of these reservoirs, which are called fractal reservoirs [8][9][10][11].…”

Semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model

“…Both have been solved elsewhere for an infinite reservoir [20]. Further, analytical solutions for infinite Euclidean non-telegraphic models, τ = 0, were studied in [1,2,6]. The semi-numerical solution presented here encompasses all mentioned cases that can be derived from Eqs.…”

“…The Laplace transform (LT) method has been widely used to solve problems in several areas of science and engineering. After proper transformation of the space variable, the application of LT to dynamic models is useful for finding semi-analytic solutions for many real dynamic problems in the so-called Laplace domain [1][2][3][4][5][6][7]. Those solutions need to be inverted in order to obtain appropriate solutions in the time domain; if analytical inversion is not possible, then numerical procedures such as the Stehfest [8] or de Hoog [9] algorithms are employed.…”

“…Sometimes, just the short-or long-term system behavior is of interest, and for this purpose asymptotic approaches are commonly used to avoid the inversion needed for complete solutions [10,11]. For solute transport and fluid flow problems in porous media, such as aquifers [3], oil, and geothermal reservoirs, the LT method helps to find semi-analytic solutions [1,2,6,12], exhibiting many advantages over purely numerical procedures. The main example is where subsequent inverse modeling will be implemented in order to retrieve model parameters of interest.…”