The primary goal of this work is to demonstrate that the fractal geometry can be used to accurately model the rate and pressure performance behavior of highly heterogeneous reservoirs such as shale oil/gas reservoirs. There are multi-scale heterogeneities that can hinder modelling and diagnostic analyses, and the use of large stimulation treatments (e.g., multi-fractured horizontal wells) can further complicate the modeling of heterogeneous reservoir systems. The primary objective of this work is to provide analytical reservoir models and diagnostic interpretation relations that can be used to estimate the well and reservoir parameters for the case of a hydraulic fracture intercepting a horizontal well within a fractal reservoir. This work presents a semi-analytical solution for the pressure and rate transient behaviors of a horizontal well intercepting a single finite-conductivity fracture within a fractal reservoir considering either single or naturally-fractured/dual porosity reservoir conditions. The shape of the imposed hydraulic fracture can be either circular or rectangular. The media (the reservoir and the fracture) are "coupled" by discretizing the fracture, which defines a system of equations, the solution of which provides the pressure at any position inside the fracture. Naturally-fractured/dual porosity and anomalous diffusion effects are included by modifying the solution of the diffusivity equation for the reservoir in the Laplace domain. The diagnostic signatures (i.e., the pressure derivative functions) for the proposed semi-analytical solution illustrate the following features: • Period 1 (Fracture flow): Radial or linear flow (depending on the geometry of the fracture) at very early times. As in classic studies for the case of a single finite-conductivity fracture, this period will never be observed in practice. 2 SPE-189814-MS • Period 3 (Reservoir dominated flow): "Pseudo-Fractal" flow. This flow period is dominated by the reservoir and yields power-law behavior (i.e., a straight line in the pressure drop and pressure derivative functions versus time on a log-log plot). In this "mechanistic"-style of study, we found that the heterogeneities of the reservoir represented by the fractal parameters, and/or the characteristics of the fracture itself can distort the pressure response during early/very early-times. Specifically, this work shows that the interaction between the fracture and the fractal reservoir can exhibit power-law pressure drop and pressure drop derivative signatures which are different from the distinctive one-quarter slope expected for bilinear flow. The following contributions are derived from this work: • Proposed solution for the pressure drop and pressure drop derivative behavior of a horizontal well intercepting a hydraulic fracture within a fractal reservoir that exhibits several "power-law" flow regimes. • Proposed features from our analytical solution for the characteristic early-time pressure drop and pressure drop derivative responses that may be of use in the diagnost...
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. 1. A well producing at a constant-rate and closed matrix blocks, 2. A well producing at a constant-rate and "infinite-acting" matrix blocks, and 1. We have found that the assumption of a well producing at variable-rate (time-dependent inner boundary condition) has a more significant impact on the pressure (and derivative) functions and hinders the effects of the properties of the reservoir. 2. We have demonstrated that the anomalous diffusion phenomena in unconventional reservoirs can be related to their multi-porosity nature. 3. The pressure and pressure derivative responses may be used in the diagnosis of flow periods and the evaluation of reservoir parameters in unconventional reservoirs.
The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents of this paper have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, or timeliness of any information herein. All information is the responsibility of, and, is subject to corrections by the author(s). Any person or entity that relies on any information obtained from this paper does so at their own risk. The information herein does not necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper by anyone other than the author without the written consent of URTeC is prohibited.
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