Summary
Surface-deformation measurements have been used for years in oil fields to
monitor production, waterflooding, waste injection, steam flooding, and cyclic
steam stimulation (CSS). They have been proved to be a very effective way to
monitor field operations and save money for operators wishing to avoid unwanted
surface breeches, casing failures, and excessive subsidence because of
production. This paper demonstrates that more information can be extracted from
surface-deformation measurements by inverting the surface deformation for the
volumetric deformation at the reservoir level using the inversion techniques
from the literature, so that the areal distribution of volumetric deformation
can be identified. This leads to a better understanding of reservoir behavior
and also provides additional data for integration into coupled reservoir
simulation modeling. This paper shows the results of mapped reservoir volume
changes from two cyclic steam injection projects using tiltmeter-based surface
deformation measurements.
Introduction
In the past fifty years oil companies and individual researchers have
studied surface deformation caused by the fluid injection into or withdrawal
from the reservoir. These studies focus mainly on three areas.
The first area of study is how to measure the surface deformation. The three
most common methods used to measure the surface deformation are
optical-instrument leveling surveys, or global positioning system (GPS) surveys
(Brink et al. 2002); interferometric synthetic aperture radar (InSAR) (Brink et
al. 2002); and tiltmeter-based surface deformation monitoring (Davis et al.
2001, 2000). Each technique has advantages and disadvantages—and in some cases,
two or even all three can be used in combination to get the required precision,
spatial coverage, and temporal resolution. Only tilt data measured by
tiltmeters is used to analyze the case studies in this paper.
The second area of study is forward modeling to predict the subsidence. Two
methods are used: numerical modeling and analytical/semianalytical modeling.
Numerical modeling for reservoir compaction and surface subsidence usually
involves the finite element method (FEM). Researchers use either the FEM or
nonlinear FEM (Plischke 1994; Abdulraheem et al. 1993; Chin et al. 1993; Bruno
and Bovberg 1992; Hamilton et al. 1992; Lewis and Sukirman 1993). The
analytical/semianalytical method refers to the use of the basic solution
because of the center of dilation source (Mindlin and Cheng 1950) or numerical
integration of the Green’s function because of the center of dilation source
over certain reservoir shapes in a poroelastic medium (Geertsma 1966, 1973;
Segall 1985). Compared to the analytical/semianalytical method, the FEM is a
general method that can handle complex material rheology, reservoir geometry,
and inhomogeneity. Drawbacks include the effort required to adequately
characterize complex constitutive models and develop stable mesh attributes.
The uncertainties involved in the rock- and fluid-property measurements might
limit the quality of the results from the FEM model. Also, the computation
expense required for complex simulations typical of the FEM can make the
repetitive calculations required in inversion modeling impractical. In this
paper, the semianalytical approach is adopted in forward modeling.
The third area of study is the inversion of the surface-deformation
measurements (displacement or tilt) for reservoir parameters (pressure
depletion, reservoir compaction, or reservoir volume changes) (Dusseault and
Rothenburg 2002; Vasco et al. 1998; Fokker 2002; Du and Olson 2001; Marchina
1996; Morita 2003). The penalty function method, or regularization method, with
constraints (smoothness or a priori model constraint), is the most commonly
used method in the industry to solve the ill-posed inverse problem. It has been
applied to obtain the pressure or volume changes (Dusseault and Rothenburg
2002; Vasco et al. 1998; Fokker 2002; Du and Olson 2001). Also, there are other
methods, such as the singular value decomposition (SVD), the stochastic
inversion method with the a priori model constraint (Marchina 1996), and
Potter’s algorithm (Morita 2003), which were applied to solve reservoir
compaction. In this paper, the penalty function with smoothness constraint and
the positive/negative constraint are used as the inversion technique. More
details about this technique could be found in the literature (Dusseault and
Rothenburg 2002; Vasco et al. 1998; Fokker 2002; Du and Olson 2001; Du et al.
1992).
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
29 August 2005
- Meeting paper published:
1 November 2005
- Revised manuscript received:
9 June 2007
- Manuscript approved:
27 June 2007
- Version of record:
25 February 2008
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