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.

Telegraphic double porosity models for head transient behavior in naturally fractured aquifers

“…In this section, we solve the boundary value problems (BVP) associated to constant head and pumping tests, common field tests used to determine the aquifer physical properties through monitoring the water discharge or head time evolution at the well [ Camacho‐Velázquez et al ., ]. In the first case, the BVP is given by equation with the head at the well radius fixed at a constant value, i.e., .…”

“…The long time asymptotic behavior and a more thorough discussion of this results when τ D = 0 can be found in Camacho‐Velázquez et al . [].…”

Analytical Solution of Fractional Order Diffusivity Equation With Wellbore Storage and Skin Effects

“…However, evidence from core, well logging, and outcrops indicate that this assumption is often not representative of such reservoirs. Application of these models to heterogeneous reservoirs with fractal behaviors in order to estimate reservoir properties, such as permeability and porosity, may lead to incorrect interpretation of the involved phenomena [1][2][3]. Euclidean models can be used if the variation of the permeability and porosity is sufficiently small compared with the interwell scale [1,4,5].…”

A Coupled Model for Fractured Shale Reservoirs with Characteristics of Continuum Media and Fractal Geometry

“…Fractional derivative was proposed by Metzler et al (2000) to describe the associated anomalous diffusion in complex/or disordered fractal media, which was the extension of O' Shaugnessy and Procaccia (1985). Subsequently, the rate response of NFRs during the transient-and boundary-dominant flow period was identified by Camacho-Velázquez et al (2008). Using the concept of induced permeability field, where varying degrees depends on the distance from the main fracture plane, Fuentes-Cruz et al (2014a) analyzed the behavior of production data of multi-fractured horizontal well.…”

“…These works mentioned above put emphasis on either identifying flow regime of production well with different fracture-geometry structures or analyzing fractal-model parameters from well testing data in naturally fractured reservoirs (Chang and Yortsos, 1990;Camacho-Velázquez et al, 2008). Cossio et al (2013) was creatively to combine fractal diffusivity equation with the trilinear flow model.…”