﻿ HFM: Hierarchical Fracture Models

## MRST - MATLAB Reservoir Simulation Toolbox

HFM: Hierarchical Fracture Models
The hierarchical fracture module (HFM) utilises the hierarchical fracture modelling framework to simulate multiphase flow in naturally fractured reservoirs with multiple length scales. Also known as the embedded discrete fracture model, this method models fractures explicitly, as major fluid pathways, and benefits from independent definitions of the fracture and matrix grid. As a result, intricate fracture networks can be modelled easily, without the need for a complex underlying matrix grid that is conformal with each fracture. The module also extends the newly developed multiscale restriction smoothed basis (MsRSB) method to compute the flux field developed in a fractured reservoir. The multiscale approach of dealing with fractures is inspired by similar strategies developed for the multiscale finite volume (MSFV) method.

## Tutorials

### Introduction: 1-phase

In this first introductory example to the HFM module, we consider a single-phase 2D example with Dirichlet boundary conditions and a horizontal central fracture in the centre. The example shows the effect of a single fracture on the reservoir pressure distribution. Moreover, the pressure solution obtained using an embedded discrete or hierarchical fracture model is compared to the results obtained from a fully resolved simulation where the fracture and matrix grid blocks are of the same size.

### 2-phase quarter-five spot

In this second introductory example to the HFM module, we show the impact of fractures on fluid migration using the embedded fracture model. To this end, we consider a two-phase example with three intersecting fractures in the center of the model. Oil is recovered by a production well in the NE corner, which is supported by a water-injector in the SW corner.

### Gas injection problem

In this example, we consider the same setup as in the two-phase example with wells, except that we now assume a three-phase, compressible model with gas injection. For comparison, we also simulate injection in the same reservoir geometry without (embedded) fractures. The purpose of the example is to demonstrate how the methods from the HFM module easily can be combined with solvers from the ad-blackoil module.

### Introduction to F-MsRSB

In this example, we will introduce you to the multiscale restriction smoothed basis (MsRSB) method for computing flow in embedded fracture models. To this end, we consider a 2D single-phase example with two intersecting fractures and Dirichelet boundary conditions. The flow problem is solved both by a fine-scale and a multiscale solver.

### F-MsRSB: 2-phase problem

Incompressible two-phase problem with water injection from the left boundary of a square domain and production at the opposite face. The grid contains 2 intersecting fractures. The flow problem is solved both by a fine-scale and a multiscale solver.

### F-MsRSB: Q5-spot

Two-phase example modeling water injection through a quarter-five spot into a 2-dimensional fractured porous media. The flow problem is solved both by a fine-scale and a multiscale solver.

### F-MsRSB: Outcrop model

Two-phase example modeling water injection into a highly fractured oil-filled reservoir. The fracture-network has been extracted from an outcrop model taken from Bisdom et al. [2].

### Water injection into 3D fractured medium

Two-phase example with a horizontal producer and injector simulating water injection in a 3-dimensional fractured porous media using the HFM module. Note that the 3D solvers are not capable of handling intersecting fracture planes.

## Description

This module has been developed by Swej Shah from Delft University of Technology in collaboration with researchers at SINTEF. The module utilises a hierarchical fracture modelling (HFM) framework to simulate multiphase flow in naturally fractured reservoirs with multiple length scales.

## Literature

1. S. Shah, O. Møyner, M. Tene, K.-A. Lie, and H. Hajibeygi. The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB). J. Comput. Phys., Vol. 318, pp. 36-57, 2016. DOI: 10.1016/j.jcp.2016.05.001
2. K. Bisdom, B. D. M. Gauthier, G. Bertotti, N. J. Hardebol. Calibrating discrete fracture-network models with a carbonate three-dimensional outcrop fracture network: Implications for naturally fractured reservoir modeling. AAPG Bulletin, 24 (2014) 1351-1376.

Published December 8, 2016