Summary
The use of ensemble Kalman filter techniques for continuous updating of
reservoir model is demonstrated. The ensemble Kalman filter technique is
introduced, and thereafter applied to a simplified 2-D field model, which are
generated by using a single horizontal layer from a North Sea field
model. By assimilating measured production data, the reservoir model is
continuously updated. The updated models give improved forecasts and the
forecasts improve as more data is included. Both dynamic variables, such as
pressure and saturations, and static variables, such as the permeability, are
updated in the reservoir model.
Introduction
In the management of reservoirs, it is important to utilize all available
data in order to make accurate forecasts. For short time forecasts, in
particular, it is important that the initial values are consistent with recent
measurements. The ensemble Kalman filter1 is a Monte Carlo approach, which is
promising with respect to achieving this goal through continuous model updating
and reservoir monitoring.
In this paper, the ensemble Kalman filter is utilized to update both static
parameters, such as the permeability, and dynamic variables, such as the
pressure and saturation of the reservoir model. The filter computations are
based on an ensemble of realizations of the reservoir model, and when new
measurements are available, new updates are obtained by combining the model
predictions with the new measurements. Statistics about the model uncertainty
is built from the ensemble. When new measurements become available, the filter
is used to update all the realizations of the reservoir model. This means that
an ensemble of updated realizations of the reservoir model is always
available.
The ensemble Kalman filter has previously been successfully applied for
large-scale nonlinear models in oceanography2 and hydrology3. In those
applications, only dynamic variables were tuned. Tuning of model parameters and
dynamic variables was done simultaneously in a well flow model used for
underbalanced drilling4. In two previous papers5,6, the filter has been used to
update static parameters in near-well reservoir models, by tuning the
permeability field. In this paper, the filter has been further developed to
tune the permeability for simplified real field reservoir simulation
models.
We present results from a synthetic, simplified real field model. The
measurements are well bottom-hole pressures, water cuts and gas/oil ratios. A
synthetic model gives the possibility of comparing the solution obtained by the
filter to the true solution, and the performance of the filter can be
evaluated. It is shown how the reservoir model is updated as new measurements
becomes available, and that good forecasts are obtained. The convergence of the
reservoir properties to the true solution as more measurements becomes
available is investigated.
Since the members of the ensemble are updated independently of each other,
the method is very suitable for parallel processing. It is also conceptually
straightforward to extend the methodology to update other reservoir properties
than the permeability.
Based on the updated ensemble of models, production forecasts and reservoir
management studies may be performed on a single "average" model, which
is always consistent with the latest measurements. Alternatively, the entire
ensemble may be applied to estimate the uncertainties in the forecasts.
Updating reservoir models with ensemble Kalman filter
The Kalman filter was originally developed to update the states of linear
systems to take into account available measurements7. In our case, the system
is a reservoir model, using black oil, and three phases (water, oil and gas).
For this model, the solution variables of the system are the pressure and the
water saturation, in addition to a third solution variable that depends on the
oil and gas saturation. If the gas saturation is zero, the third solution
variable becomes the solution gas/oil ratio, if the oil saturation is zero it
becomes the vapor oil/gas ratio. Otherwise the third solution variable is the
gas saturation. The states of this system are the values of the solution
variables for each grid block of the simulation model. This model is
non-linear.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
4 June 2003
- Revised manuscript received:
8 November 2004
- Manuscript approved:
18 January 2005
- Version of record:
15 March 2005
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