Summary
This paper applies the ensemble Kalman filter (EnKF) to history match a
North Sea field model. This is, as far as we know, one of the first published
studies in which the EnKF is applied in a realistic setting using real
production data. The reservoir-simulation model has approximately 45,000 active
grid cells, and 5 years of production data are assimilated. The estimated
parameters consist of the permeability and porosity fields, and the results are
compared with a model previously established using a manual history-matching
procedure. It was found that the EnKF estimate improved the match to the
production data. This study, therefore, supported previous findings when using
synthetic models that the EnKF may provide a useful tool for history matching
reservoir parameters such as the permeability and porosity fields.
Introduction
The EnKF developed by Evensen (1994, 2003, 2007) is a statistical method
suitable for data assimilation in large-scale nonlinear models. It is a Monte
Carlo method, where model uncertainty is represented by an ensemble of
realizations. The prediction of the estimate and uncertainty is performed by
ensemble integration using the reservoir-simulation model. The method provides
error estimates at any time based on information from the ensemble. When
production data are available, a variance-minimizing scheme is used to update
the realizations. The EnKF provides a general and model-independent formulation
and can be used to improve the estimates of both the parameters and variables
in the model. The method has previously been applied in a number of
applications [e.g., in dynamical ocean models (Haugen and Evensen 2002), in
model systems describing the ocean ecosystems (Natvik and Evensen 2003a,
2003b), and in applications within meteorology (Houtekamer et al. 2005)]. This
shows that the EnKF is capable of handling different types of complex- and
nonlinear-model systems.
The method was first introduced into the petroleum industry in studies
related to well-flow modeling (Lorentzen et al. 2001, 2003). Nævdal et al.
(2002) used the EnKF in a reservoir application to estimate model permeability
focusing on a near-well reservoir model. They showed that there could be a
great benefit from using the EnKF to improve the model through parameter
estimation, and that this could lead to improved predictions. Nævdal et al.
(2005) showed promising results estimating the permeability as a continuous
field variable in a 2D field-like example. Gu and Oliver (2005) examined the
EnKF for combined parameter and state estimation in a standardized reservoir
test case. Gao et al. (2006) compared the EnKF with the
randomized-maximum-likelihood method and pointed out several similarities
between the methods. Liu and Oliver (2005a, 2005b) examined the EnKF for facies
estimation in a reservoir-simulation model. This is a highly nonlinear problem
where the probability-density function for the petrophysical properties becomes
multimodal, and it is not clear how the EnKF can best handle this. A method was
proposed in which the facies distribution for each ensemble member is
represented by two normal distributed Gaussian fields using a method called
truncated pluri-Gaussian simulation (Lantuéjoul 2002). Wen and Chen (2006)
provided another discussion on the EnKF for estimation of the permeability
field in a 2D reservoir-simulation model and examined the effect of the
ensemble size. Lorentzen et al. (2005) focused on the sensitivity of the
results with respect to the choice of initial ensemble using the PUNQ-S3.
Skjervheim et al. (2007) used the EnKF to assimilate seismic 4D data. It was
shown that the EnKF can handle these large data sets and that a positive impact
could be found despite the high noise level in the data.
The EnKF has some important advantages when compared to traditional assisted
history-matching methods; the result is an ensemble of history-matched models
that are all possible model realizations. The data are processed sequentially
in time, meaning that new data are easily accounted for when they arrive. The
method allows for simultaneous estimation of a huge number of poorly known
parameters such as fields of properties defined in each grid cell.
By analyzing the EnKF update equations, it is seen that the actual degrees
of freedom in the estimation problem are limited equal to the ensemble size.
One is still able to update the most important features of large-scale models.
A limitation of the EnKF is the fact that its computations are based on first-
and second-order moments, and there are problems that are difficult to handle,
particularly when the probability distributions are multimodal (e.g., when
representing a bimodal channel facies distribution).
This paper considers the use of the EnKF for estimating dynamic and static
parameters, focusing on permeability and porosity, in a field model of a
StatoilHydro-operated field in the North Sea. The largest uncertainty in the
model is expected to be related to the permeability values, especially in the
upper part of the reservoir where the uncertainty may be as large as 30%.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
28 June 2006
- Meeting paper published:
24 September 2006
- Revised manuscript received:
30 May 2008
- Manuscript approved:
9 June 2008
- Version of record:
15 December 2008
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