Page 373 - Numerical Analysis and Modelling in Geomechanics

354 RESERVOIR COMPACTION, SUBSIDENCE AND WELL DAMAGE
water, and gas production, and water injection. Some details of the reservoir flow
modeling were presented by Fredrich et al. 40 Hydraulic fracturing introduces
considerable heterogeneity and anisotropy to the reservoir pore pressure field.
The flow model was history-matched to volumetric data from production and
injection wells. For the two-dimensional models to capture the spatial effects of
the pore pressure field (e.g., the effects of the hydraulic fracturing), pore
pressures from the three-dimensional model were averaged over 12 grid blocks
perpendicular to the plane of the model and projected onto the nodal coordinates.
Pore pressures were prescribed only on elements corresponding to the delineated
reservoir, which is confined in Figure 11.7 to the center of the model in the
lightly shaded elements which represents the diatomite and upper porcelanite
layers.
The two-dimensional, field-scale finite element modeling was performed as a
quasi-static analysis. Reservoir pore-pressure fields computed in the flow model
were prescribed as boundary conditions on the nodes of the finite element model.
Displacement boundary conditions on lateral edges and the bottom of the model
were also prescribed.
The 18-year field history was simulated in nineteen steps. The first step
developed the geostatic, or tectonic, in situ stress field. In this first step, pore
pressures were prescribed to be 0 psi. The vertical stress at any depth was computed
from the unit weight of the rock. The horizontal stress factors in Equation (11.
44) were taken to be K =0.80 and K =1.20. These factors were determined
oH
oh
from studies of regional tectonic stresses in the Belridge field. 32,95 Since the
materials are elastoplastic and the geologic layering is not purely horizontal, the
computation of initial stresses was not straightforward. A trial-and-error
procedure was developed to compute the in situ stress field. After the geostatic
stress step was completed, pore pressures were changed incrementally for each
year of the 18-year simulated field history.
As noted, pore pressures were prescribed as boundary conditions, hence the
change in the state of effective stress was not the result of deformation of pores or
changes in permeability of the rock. In this sense, this geomechanical analysis
was not fully coupled. The elastoplastic deformation of the rock was in response
to the change of effective stress. A fully coupled analysis would include the
coupling between transient flow of pore fluids and pore deformations.

Computational results
As discussed earlier, modeling was performed on two scales, that of the reservoir
and that of an individual well, with two separate computational models.
Computations from these models and comparisons to historic field measurements
and data are described in this section.