Dual Continuum Fluid Flow Simulation in Stress Sensitive Naturally Fractured Reservoirs

Abdul Ravoof Shaik, Mohammad Ali Aghighi, Nam H. Tran, Altaf H. Syed and Sheikh S. Rahaman
School of Petroleum Engineering, University of New South Wales, Sydney NSW 2052 - AUSTRALIA
Keywords: Flow simulation, Naturally fractured reservoir, Unsteady state, Deformation, Dual continuum.
ABSTRACT: Fluid flow simulation for naturally fractured reservoirs is a significant and challenging task. A large
part of the world’s remaining hydrocarbon reserves are contained within such reservoirs. Recent advancement in
fracture characterization techniques could result in very comprehensive discrete fracture network models.
However, the models’ arbitrary fracture size, orientation and spatial distribution create complex flow paths and
heavy computational workload for a simulation program. The complexity is further raised, taking into account the
effect of field stresses on the deformable fractures and rock. Previous reservoir simulation works did not
incorporate these multiple facies of a detailed geological modeling in their production forecast.
In the present work, a fracture network has been generated from author’s previous work, combining statistical and
spatial analyses, object-based modelling and conditional global optimization. For purpose of fluid flow simulation,
Fractures are treated as discrete objects based on their length and each fracture is modeled implicitly and
upscaled using grid based permeability tensor concept. A dual continuum fluid flow simulation model is developed
and validated, which is able to handle fluid flow between matrix-fracture, matrix-matrix, and fracture- fracture and
effects of deformation. In this work, the geomechanics solution is decomposed into matrix and fracture parts and
used to compute their dynamic porosity and permeability separately.
The model is validated against analytical data and data published in literature. The results show that the model
can overcome problems existing in previous models in relation to computational resources, flow interactions
between matrix and fracture and effect of deformation on fluid flow. The examples show that deformation has a
major impact on productivity or injectivity, and the need of integrated fracture modelling for more accurate
production forecasting.
1 Introduction
Naturally fractured reservoirs (NFR) contain a large percentage of world’s oil and gas reserves. Production
forecast from such a complicated and highly heterogeneous formation is extremely difficult. Comprehensive and
reliable fluid flow simulation is essential for development of naturally fractured reservoirs. Numerical fluid flow
simulation for spatially distributed fractured network is very challenging. To add complexity to the matter, reservoir
properties are strongly related to rock deformation during the course of production. For example, the
experimental work carried out by Stone. et al. (2003) shows that there is 20% or more reduction in permeability
due to rock deformation. The reservoir properties are affected by change in effective stresses due to fluid
production and/or injection, which result in opening and closure, and reorientation of fractures. These variations in
geomechanical behaviour of reservoir, affect the permeability, which is a controlling factor in production
forecasting of naturally fractured reservoirs.
The motivation of this research is to observe the effect of geomechanics on fluid flow simulation in both naturally
and induced fractured networks. Simulation of NFR requires a comprehensive understanding of complex issues
like, coupling between geomechanics and fluid flow, mechanics of rock deformation, grid block representation of
fractured rocks, stress sensitive fracture/ matrix permeability, and coupled and uncoupled fluid flow models.
Previous fluid flow models for naturally fractured reservoirs neglect the effect of geomechanics on the reservoir
productivity, or simplified it by ignoring the non-orthogonal fractures. Porosity/ permeability are typically treated as
a constant through the reservoir life, which lead to inaccurate production forecasts. The following two subsections
discuss the methods applied in literature to date, followed with their limitations.
1.1 Fluid flow simulation methods
Fluid flow through fractured porous medium to date can be divided into three different types, single continuum,
dual continuum, discrete fracture approach and tensor approach. In the single continuum approach, fracture
medium is represented by an equivalent porous medium and it results in very low accuracy as this approach does
not consider the fracture geometry. Dual continuum approach is further divided into dual porosity and dual
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porosity/permeability model. In dual porosity models, matrix permeability neglected, in other words fluids don’t
flow directly from one matrix block to another. Recently, tensor approach has been became very popular in recent
years, which is able to simulate complex intersecting fracture network with better accuracy and low computational
requirements. This is a mixed concept of dual porosity/permeability approach and discrete fracture approach,
where effective permeability tensor is used to simulate the fluid flow. This approach is developed by Teimoori et
al. (2004), based on hierarchical concept used in previous simulation models of Lee et al. (1999), Lee et al.
(2001), Lough et al. (1997) , where a grid block with fractures has been replaced by a homogenous grid block
having an equivalent permeability tensor. Common draw back of all these models is they ignored the effect of
stress on fluid flow, which is very important if rock is stress sensitive.
1.2 Effect of geomechanics
Effect of geomechanics on fluid flow has come into attention of petroleum engineers, which could extensively
affect total cumulative production, reserves estimates, profitability and so on. Well bore stability, hydraulic
fracturing, waste water and solid injection, sand production and subsidence are some of the phenomena that can
be modelled effectively only by stress coupled simulator.
Terzaghi (1943) initiated analysis of fluid flow and stress coupling. Later, Boit (1957) extended the stress coupling
theory into three dimensional case, based on a linear stress-stain relation a single-phase fluid. In the literature,
different approaches have been proposed to extend Biot’s single porosity theory to dual porosity and discrete
models. Simulating fluid flow in complex reservoirs using fully coupled algorithm gives accurate results
theoretically, but it is very time consuming and cost effective. To overcome the above mentioned limitations,
Minkoff, et al. (2003) proposed a loose algorithm, which updates geo-mechanical properties at distinctive time
steps. While coupling ground water with surface water, Layton et al. (2003) used Stokes equation in the fluid
region with Darcy’s equation in the porous medium and Beavers-Joseph-Saffman condition for interface. Tran et
al. (2005)’s iteratively coupled fluid flow simulation model uses stress dependent porosity function. Reservoir
porosity is treated as intermediate unknown from geomechanics equation to the reservoir flow equations, which is
expressed as a function of true porosity and the volumetric strain. Authors showed that, displacements as well as
the porosity calculations depend not only on the stress response but also on the constitutive law of a material.
Recently, the advantage of joint mechanics theory to develop general, rigorous coupling between fluid flow
equation and deformation of fractured media is applied in Bagheri et al. (2006)’s simulation. Authors made
successful attempt in decomposing geomechanics solution into matrix and fracture parts and used to compute
their dynamic porosity and permeability separately. But this work did not address spatially fractured reservoir.
In literature, most of the previous fluid flow models are suffering limitations such as need of high computational
resources, deals with uniform/oblique fracture network only, matrix-matrix flow or matrix-fracture flow ignore, used
empirical equations to include stress dependency and ignored/unable to handle effect of connected/ intersected
fractures. To address the above mentioned issues in fluid flow simulation, a fracture network has been generated
using combining statistical and spatial analyses, object-based modelling and conditional global optimization,
developed by Tran. et al. (2006), One of the authors for this report. Effective permeability tensor concept is
applied to investigate the effect of geomechanics on fluid flow through the complex fracture network.
2 Methodology
The aim of this research is to observe the effects of rock deformation on fluid flow in spatially fractured reservoirs.
To accomplish this, a numerical code has to be developed to simulate fluid flow through arbitrary fractured
network while considering flow through fracture, matrix and through interface, and it has to be coupled to
geomechanics model to embrace the effect of rock deformation. Three numerical models are developed and
coupled iteratively in the end. Partial coupling strategy is chosen to minimize computational sources.
In the first numerical model (Tensor module), where boundary element method is applied to calculate grid block
permeability, tensor is calculated using periodic boundary condition. The second numerical model, Flow module
is developed using finite element method, to calculate unsteady state fluid flow from effective permeability tensor
map. Finite element method is applied to develop the third numerical model (Deformation/coupling module) to
update rock properties. Implementation of the proposed approach is shown schematically in Fig 1. This flowchart
highlights the stages of calculation of fracture and matrix flow properties and the way they are coupled to the
deformation module. In the initial stage, matrix and fracture properties are transferred to the tensor module in
each iteration loop to build an effective permeability tensor. Flow module uses the permeability tensor for fluid
flow simulation. Fracture/ matrix properties are calculated at each iteration using the deformation model, and they
are passed on to the tensor module for dynamic permeability tensor calculations.
2.1 Numerical modelling
This research addresses non orthogonal fractured reservoir fluid flow simulation, covering two important subaspects:
(1) fluid flow through the system of rock matrix, interconnected fractures and inter-flow across matrix-

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