Abstract

The paper shows a way to provide a detailed description of conditions in the hydraulically damaged fracture environment after closure and how to integrate it into a reservoir simulation model.

A special model initialization algorithm was developed and realized in a support tool to make possible the computing a post-fracture performance in tight gas formations by a reservoir simulator. The input represents the treatment schedule of the fracturing process and some results produced by commercial fracturing packages or geophysical measurements.

To represent the fracture geometry and properties, the information about the distribution of the proppant concentration in the fracture as well as fracture width variation is translated into the permeabilities and porosities of the fracture gridblocks. To determine the fracturing fluid saturation in the invaded zone, a new approach was derived to imitate the fracture propagation at a fracturing period under consideration of the leakoff processes. The penetration of the fracturing fluid into the matrix was modeled by Buckley-Leverett equations for two-phase non-miscible displacement with boundary conditions provided by a classical leakoff theory.

The approach is illustrated with a simulation model prepared to the analysis of the cleanup process in a damaged fractured well within a Rotliegende tight gas formation in North Germany.

Introduction

The fluid leaked off into the tight gas formation during the fracturing treatment may significantly suppress gas production due to the two-phase flow effects and the capillary end effect between the reservoir and fracture.1 Therefore, for more plausible evaluation of hydraulic fracture stimulation, an accurate representation considering the flow in the immediate fracture environment becomes a necessity. In terms of numerical simulation of post-fracture well performance, the problem can be addressed by

  1. an adequate representation of the fracture in a reservoir simulator and

  2. a reasonable accurate picture of the initial fluid distribution around the fracture.

The present work is focused on these two main points which are explained bellow.

1. In our previous paper2 we gave a comprehensive comparison analysis of different approaches to numerical modeling of the fractured wells in tight reservoirs. Among them are:

  1. Fracture is considered by a series of high permeability grid blocks of a reservoir model;

  2. Separated reservoir and fracture models are coupled through the source/sink term;

  3. Fracture is presented by modification of the transmissibilities of the reservoir gridblocks containing the fracture.

It was shown that the first, more traditional technique with a reasonable local grid refinement can be a preferable method when the flow under study does not contain any features making difficult to simulate within the framework of a reservoir model. So, the present work was oriented to the use of a conventional reservoir simulation program.

The integration of the fracture into the reservoir model is not a problem of great concern. A short discussion of this may be found, e.g., in Settari et al.3, Banerjee et al.4. Reasoning of the time step limitation and because of Peaceman's condition for structured orthogonal grids, the fracture in the model can not take the actual width. Correspondingly, the permeability and porosity of the fracture blocks are reduced in order to maintain the transmissibility and porous volume of the fracture. The starting values of the hydraulic parameters within the fracture are calculated from the proppant distribution after the closure. These data can be obtained by the fracturing simulation with consideration of proppant transport processes or indirect, geophysical measurements.

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