Summary
The application of elastic stress simulation for fracture modeling provides
a more realistic description of fracture distribution than conventional
statistical and geostatistical techniques, allowing the integration of
geomechanical data and models into reservoir characterization. The
geomechanical prediction of the fracture distribution accounts for the
propagation of fracture caused by stress perturbation associated with faults.
However, the challenge lies in estimating the past remote stress conditions
which induced structural deformation and fracturing, the limited applicability
of the elasticity assumption, and the latent uncertainty in the structural
geometry of faults. The integration of historical production data and well-test
permeability into geomechanical fracture modeling is a practical way to reduce
such uncertainty. We propose to combine geostatistical algorithms for history
matching with geomechanical elastic simulation models for developing an
integrated yet efficient fracture modeling tool.
This paper presents an integrated approach to history matching of naturally
fractured reservoirs which includes (1) fracture trend prediction through
elastic stress simulation; (2) geostatistical population of fracture density
based on a fracture trend model; (3) fracture permeability modeling integrating
fracture density, matrix permeability and well-test permeability; and (4)
numerical flow simulation and history matching. All of these implementations
are incorporated into a single forward modeling process and iterated in the
automatic history-matching scheme. To obtain a history match on a reservoir
model, we jointly perturb the large-scale fracture trend and local-scale
geostatistical fluctuations of fracture densities rather than perturbing
permeability calibrated from fractures. This strategy enables us to preserve
the geological/geomechanical consistency throughout the history-matching
process. The geomechanically simulated fracture trend model is calibrated to
both production data and the reservoir geological structure (faults and
horizons) by searching for the optimum remote stress condition for elastic
stress-field simulation. The latter is achieved by matching the actually
observed structural deformation with the simulated one. The smaller-scale
fluctuation of fracture density is simultaneously history matched through the
probability perturbation method of Caers (Caers 2003; Hoffman and Caers 2005;
Caers 2007). The methodology is presented on a synthetic reservoir
application.
Introduction
The modeling of the density and pattern of fracture distributions can take
different approaches depending on the origin and the type of fracture sets and
on the ultimate reservoir engineering questions raised. In this paper, we focus
on the modeling of shear fractures which are generated by structural
deformation accompanied with fault slip. Recently, an application of the
elastic stress simulation has been proposed for predicting the pattern of
shear/tensile fractures or the pattern of secondary faults and shown promising
results (Bourne and Willemse 2001; Maerten et al. 2002; Bourne et al. 2001).
The elastic simulation numerically simulates the structural deformation of the
reservoir by solving linear elasticity equations under given boundary
conditions, and simultaneously calculates the corresponding stress/strain
tensor fields (Bourne and Willemse 2001; Maerten et al. 2002; Bourne et al.
2001; Daly and Mueller 2004; Roxar FracPerm Reference Manual 2005). The
boundary conditions consist of (1) location/geometry of fault surface, (2)
stress conditions or displacement conditions on the fault surfaces, and (3) the
remote loads applied to the structure at the time of structural deformation
accompanied with fault slippage. First, satisfying boundary conditions and by
minimizing strain energy, the linear elastic equations are solved to obtain a
structural deformation field which is expressed by the displacement vector.
Next, strain field is computed from the displacement gradient based on the
definition of strain. Finally, under the assumption of elasticity, stress is
calculated from strain by means of Hook’s law.
© 2007. Society of Petroleum Engineers
View full textPDF
(
2,118 KB
)
History
- Original manuscript received:
13 July 2005
- Meeting paper published:
9 October 2005
- Revised manuscript received:
17 August 2006
- Manuscript approved:
6 September 2006
- Version of record:
20 March 2007
View Cart
