Abstract
The major contribution of this paper is the description of an efficient,
gradient-based method for incorporating time-lapse seismic impedance data in an
automatic history matching procedure. We use a finite-difference, black-oil
reservoir simulator, with rock physics included, to predict seismic impedance
as a function of saturation and pressure. The adjoint method is used to compute
the derivatives of seismic impedance change in each gridblock with respect to
porosity, permeability, pressure and phase saturation. With a quasi-Newton
minimization method to efficiently minimize the difference between observed
impedance changes and the impedance changes predicted using the reservoir
simulator, our procedure can be applied to field-scale problems. The
feasibility of this method of utilizing time-lapse seismic data is illustrated
with an application to a semi-synthetic model created from a relatively large
middle-eastern oil field.
Introduction
Time-lapse seismic is the process of repeating 3D seismic surveys over a
producing reservoir to monitor changes in saturation and pressure. The
potential impact on reservoir engineering and reservoir management is large
because time-lapse seismic may allow direct imaging of rock properties that are
closely related to vertically averaged fluid saturations and pressure. This is
much different from the current limitation of measurements of these quantities
at well locations. In general, seismic images are sensitive to the spatial
variation of both static properties (lithology, shale content, etc.) and
dynamic fluid-flow properties (fluid saturation, pore pressure, etc.)1. If data
were available from only one 3D seismic survey, it would not be possible to
differentiate between the effects of static features and those due to changes
in saturation and pressure. If, however, data from two seismic surveys shot at
different times were compared, the effects from the static features could be
significantly reduced and the dynamic changes emphasized. Since the dynamic
changes in pressure and saturation are indirectly related to permeability and
porosity in the reservoir, it seems reasonable to use the time-lapse seismic
data with automatic history matching to quantitatively estimate those
parameters.
The simplest, most direct method of using time-lapse seismic data is to
qualitatively monitor reservoir changes due to production. In this approach,
one simply identifies regions in which the amplitude or impedance has changed
with time and attributes these changes to changes in saturation, pressure, or
temperature. The first tests of this concept were carried out by ARCO in the
Holt Sand fireflood from 1981 to 19832. Similar studies have been reported by
Cooper3 at the Foinhaven field, Lumley4 at the Meren field in Nigeria and
Behrens5 at Bay Marchand. The primary objectives at Foinhaven were simply to
map fluid movements and to identify by-passed oil. The authors of the study
concluded that the time-lapse signal qualitatively agreed with the expected
reservoir performance. At Meren, the goal was to identify pathways of injected
water, sealing faults, and compartments that may contain by-passed oil. For Bay
Marchand, time-lapse seismic was used to monitor water flux and identify the
by-passed oil. Moreover, the analysis provided a qualitative comparison of the
quality of seismic data before and after cross-equalization, which is a very
important step in time-lapse seismic data processing. The authors concluded
that the data allowed these objectives to be achieved.
The other, more difficult, approach is to use the time-lapse seismic data in
an automatic history matching procedure to estimate the reservoir flow
parameters, such as permeability and porosity6,7,8. Traditionally, automatic
history matching attempts to honor observed production data, such as bottom
hole pressure ( ), gas-oil ratio (GOR), and water-oil ratio (WOR), while
maintaining the geological plausibility of the model. If, however, the number
of production data is small compared to the number of model parameters, the
resulting estimates of permeability and porosity will almost certainly be
poorly constrained. Although inverse problems in general, and automatic history
matching problems in particular, are underdetermined, results derived from
small amounts of data still provide estimates that are less than satisfying. It
would clearly be beneficial to make use of some type of “space-dense” data that
would improve the resolution of the estimate in the gridblocks far away from
well locations. Among all usual data related to petroleum engineering, seismic
data is the most promising candidate for improved spatial coverage. In
addition, advances in automatic or computer-assisted history matching have
begun to allow researchers to consider the integration of time-lapse seismic
data with production data.
The type of time-lapse seismic data used for property estimation has varied
among the researchers. Huang8 used amplitude difference or other seismic
attributes difference while Arenas9 used velocity difference. Gosselin7 assumed
that pressure and saturation changes were available. Landa10 also assumed that
saturation changes could be obtained directly from time-lapse surveys. While a
number of geophysicists11,12,13 have assumed that changes in saturation and
pressure can be estimated directly from time-lapse seismic data (including
offset data), it is clearly better to work directly from the rock physics, mass
and momentum balance relationships to ensure that all data are honored. Based
on our preliminary investigation14, we chose to work with seismic impedance
change data, which is derived from time-lapse seismic. In the preliminary
study, we investigated the effect of variation of poorly constrained variables
such as clay content on seismic impedance change data directly and concluded
that seismic impedance change data would often provide useful constraints to
our history matching procedure.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
4 June 2003
- Revised manuscript received:
5 November 2004
- Manuscript approved:
15 November 2004
- Version of record:
15 March 2005
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