Transient Flow in Discretely Fractured Porous Media

Abstract

This paper presents an analytical study of transient flow into multiple vertical wells producing from a porous media containing randomly distributed discrete fractures. The model may be used to analyze the production and well test data from tight gas sands and Austin chalk type reservoirs. Both vertical openholes and hydraulically fractured vertical wells are considered. Wells and fractures are randomly distributed. The model dynamically couples the multiple fracture flow models with an analytical reservoir flow model. The analytical model simulates pressure and pressure derivative characteristics of wells and flow distribution along and through both the natural and hydraulic fractures. The study shows that single or multiple isolated fractures yield negative pseudoskin factors in vertical wells near isolated fractures. The negative pseudoskin factor in un-stimulated wells has also been observed in field tests. The negative pseudoskin factor is a function of fracture conductivity, fracture density, length, distance from the wellbore, and azimuth. Using the model, we demonstrate that the shape of pressure derivative is related to fracture distribution. However, the wellbore pressure derivative response is controlled by the fractures in the near wellbore region. The result of this study indicate that the conventional analysis, based on the double porosity model such as the Warren and Root model, to predict the storativity ratio of a naturally fractured system is not reliable. Also, the displacement between two semilog straight lines is not necessarily a good indicator of the storativity ratio. Introduction Naturally fractured reservoirs may be classified as extremely heterogeneous porous media. Modeling the fluid flow in naturally fractured reservoirs has been one of the most challenging topics in the petroleum industry throughout years. There are many naturally fractured reservoirs all around the world. A significant part of the known hydrocarbon reserves are in naturally fractured porous rocks. Therefore, building realistic models representing naturally fractured reservoirs are of vital importance to maximize hydrocarbon recovery from such reservoirs. The main focus of this study is to develop an analytical model to simulate the flow inside a homogenous porous media containing randomly distributed and unconnected fractures. Once such a model is available, the effect of isolated fractures on the pressure transient behavior of producing wells may be investigated. In the current literature, only a few analytical studies focus on the effect of stochastically distributed natural fractures on well performance. To the best of our knowledge, the literature lacks a model to simulate the transient flow towards a system of vertical openholes and hydraulically fractured wells producing from a porous media dissected by randomly distributed but disjointed natural fractures. This study offers such a model to investigate the effect of multiple isolated fractures on wellbore pressure. Literature Review The model presented in this study could be used to simulate the flow behavior in an infinite reservoir that contains naturally fractures, hydraulically fractured wells, and vertical openholes. Therefore, a summary of the current literature on each subject is presented. The literature review is divided into five different sections; multiple vertical well models, dual porosity models, hydraulic fracture models, single isolated natural fracture model, and discreet fracture network models. Multiple Vertical Well Models. The available literature on this subject is too extensive; hence, we just refer to only a few studies. Several researchers have presented flow models for multiple vertical wells producing from a common reservoir. The researchers have investigated the pressure response and inflow performance of a multiple well system in infinite and finite homogenous formations.1–7 The interference between wells in closed and infinite reservoirs have also been examined. Most of the publications concentrate on the calculation of the productivity of a multi-well system, the drainage area for each well, and the analysis of transient pressure data.3–7 Rodriguez and Cinco-Ley 1 presented a two-dimensional analytical solution for multiple vertical wells producing from closed-boundary reservoirs. Their model predicts the production performance of multiple wells producing at constant bottomhole pressure.

Parameter Prediction of Hydraulic Fracture for Tight Reservoir Based on Micro-Seismic and History Matching

“…24,25 Izadi and Yildiz simulated the transient flow of the fractured porous medium to study the effect of discrete fracture for wellbore pressure drop and infinite homogeneous reservoir pressure. 26 In the same year, Tae and David introduced fractal theory and used fractal discrete fracture network model to estimate the reservoir porosity. 27 Moinfar compared two types of DFM and dual-medium models which illustrate the significant advantages of the DFM in solving the local strong heterogeneity medium and large fractures.…”