Summary
The traditional approach to reconciling geologic models to production data
involves an “amplitude matching,” that is, matching the production history
directly. These include water-cut, tracer concentration, and pressure history
at the wells. It is well known that such amplitude matching results in a highly
nonlinear inverse problem and difficulties in convergence, often leading to an
inadequate history match. The nonlinearity can also aggravate the problem of
nonuniqueness and instability of the solution. Recently, production data
integration by “travel-time matching” has shown great promise for practical
field applications. In this approach, the observed data and model predictions
are lined up at some reference time such as the breakthrough or “first arrival”
time. Further extensions have included amplitude information by a “generalized
travel-time” inversion. Although the benefits of travel-time inversion are well
documented in the context of seismic inversion, no systematic study has been
done to examine its merits for field-scale history matching.
In this paper, we quantitatively investigate the nonlinearities in the
inverse problems related to travel time, generalized travel time, and amplitude
matching during production data integration and their impact on the solution
and its convergence. In our previous works, we speculated on the quasilinear
nature of the travel-time inversion without quantifying it. Our results here
show, for the first time, that the commonly used amplitude inversion can be
orders of magnitude more nonlinear compared to the travel-time inversion. We
also examine the resulting implications in field-scale history matching. The
travel-time inversion is shown to be more robust and exhibits superior
convergence characteristics. The travel-time sensitivities are more uniform
between the wells compared to the amplitude sensitivities that tend to be
localized near the wells. This prevents overcorrection near the wells.
We have demonstrated our results using a field application involving a
multiwell, multitracer interwell tracer injection study in the McCleskey
sandstone of the Ranger field, Texas. Starting with a prior geologic model, the
traditional amplitude matching could not reproduce the field tracer response,
which was characterized by multiple peaks. Both travel time and generalized
travel time exhibited better convergence properties and could match the tracer
response at the wells with realistic changes to the geologic model.
Introduction
Geologic models derived from static data alone often fail to reproduce the
production history of a reservoir. Reconciling geologic models to the dynamic
response of the reservoir is critical to building reliable reservoir models. In
recent years, several techniques have been developed for integrating production
data into reservoir models.1–14 The theoretical basis of these techniques is
generally rooted in the least-squares inversion theory that attempts to
minimize the difference between the observed production data and the model
predictions. This can be referred to as “amplitude” matching. The production
data can be water-cut observations, tracer response, or pressure history at the
wells. It is well known that such inverse problems are typically ill-posed and
can result in nonunique and unstable solutions. Proper incorporation of static
data in the form of a prior model can partially alleviate the problem. However,
there are additional outstanding challenges that have deterred the routine
integration of production data into reservoir models. The relationship between
the production response and reservoir properties can be highly nonlinear. The
nonlinearity can result in multiple local minima in the misfit function. This
can cause the solution to converge to a local minimum, leading to an inadequate
history match. All these can make it difficult to obtain a meaningful estimate
of the parameter field, particularly if the initial model is far from the
solution.
Recently, streamline-based methods have shown significant potential for
incorporating dynamic data into high-resolution reservoir models.1–14 A unique
feature of the streamline-based production data integration has been the
concept of a “travel-time match” that is analogous to seismic tomography.
Instead of matching the production data directly, the observed data and model
predictions are first “lined up” at the breakthrough time. This is typically
followed by a conventional amplitude match, whereby the difference between the
observed and calculated production response is minimized. A major part of the
production data misfit reduction occurs during the travel-time inversion, and
most of the large-scale features of heterogeneity are resolved at this
stage.2,4,5
The concept of travel-time inversion is not limited to streamline models.
Recently, it has been extended for application to finite-difference models
through a “generalized travel-time” inversion.9 The generalized travel-time
inversion ensures matching of the entire production response rather than just
the breakthrough times and at the same time retains most of the desirable
properties of the travel-time inversion. The concept follows from wave-equation
travel-time tomography and is very general, robust, and computationally
efficient.12,15 The generalized travel-time inversion has been utilized to
extend the streamline-based production data integration methods to changing
field conditions involving rate changes and infill drilling.
© 2005. Society of Petroleum Engineers
View full textPDF
(
3,131 KB
)
History
- Original manuscript received:
4 June 2003
- Revised manuscript received:
12 August 2004
- Manuscript approved:
12 January 2005
- Version of record:
15 March 2005
View Cart
