Page 364 - Numerical Analysis and Modelling in Geomechanics

RESERVOIR COMPACTION, SUBSIDENCE AND WELL DAMAGE 345
prevented from flowing (i.e., if the stress state is undrained). Alternatively, if the
pore pressure is increased or decreased, then the effective stress on the volume of
rock will change depending on the boundary conditions applied to the rock.
For large deformation, elastoplastic analysis of compaction, the complete set of
governing equations defines a transient nonlinear system, which must be
integrated numerically in the time domain. The system of equations is difficult to
solve even for small problems, but especially difficult for large problems, such
as a large-scale reservoir compaction simulation. The theory and numerical
solution of the nonlinear, completely coupled system by finite element methods
has been presented by a number of authors for applications in geotechnical
engineering (i.e., consolidation and liquefaction) and petroleum engineering (i.e.,
compaction). 55–57,86–88
Though the fully coupled problem is highly nonlinear, some general
observations regarding the effects of coupling can be stated. The state of stress in
the reservoir rock under compacting conditions is compression. The weight of
the overburden is the mechanism responsible for the compression, and hence
drives the compaction. Compaction, which is in part the reduction in pore
volume, drives fluid from the pores, or causes an increase of the pore fluid
pressure, if the fluid is prevented from flowing. By the same token, the stress is
affected by the pore pressure change, which affects the overall stress state in and
around the reservoir, and hence affects the amount of compaction. Both of these
effects are the salient effects of the coupling between rock deformations and pore
fluid pressure. Historically, it has been the case that most reservoir flow simulators
have no geomechanical capability, and therefore do not include coupling. That
is, the rock matrix is incompressible, though the fluid may be compressible and
multiphase. In such simulators, measured volumes of oil, water and gas,
produced or injected, are “history matched” to the wells and reservoir pressure
behavior computed with the simulator. The resulting pressure fields are used for
predicting field life and operating conditions. Yale et al. 89 implemented an
improvement to their reservoir simulator by incorporating a variable rock
compressibility into a reservoir simulator, but that modification was not an
implementation of full coupling.
In some recent case studies, the solution of the governing equations has been
simplified by assuming a steady-state solution for the pore pressure. The steady
state solution is still coupled, but the coupling is milder, without transient
effects. Computing pore pressures with a standard uncoupled reservoir simulator
been used as a further simplification. The computed pore pressures are
prescribed as pore pressure boundary conditions at discrete intervals of time
(e.g., yearly) in a nonlinear geomechanical finite element model and
deformations are computed based on the effective stress. 37–40 In this approach, a
sophisticated reservoir simulator was used to compute reservoir pressure based
on the production and the injection of literally hundreds of wells, thus a highly
heterogeneous pore pressure field was used in the finite element model to
compute compaction and its effects. However, this approach results in coupling