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Richard John Greatbatch Xiaoming Zhai Jan-Dirk Kohlmann Lars Czeschel 《Ocean Dynamics》2010,60(3):617-628
Eddy momentum fluxes, i.e. Reynold stresses, are computed for the latitude bands of the Gulf Stream and Kuroshio extensions
using 13 years of data from the merged satellite altimeter product of Le Traon et al. The spatial pattern and amplitude of
the fluxes is remarkably similar to that found by Ducet and Le Traon using the 5 years of data that were available to them.
In addition to updating the work of Ducet and Le Traon, we provide new insight into the role played by the underlying variable
bottom topography, both for determining the structure of the eddy momentum fluxes seen in the satellite data and for influencing
the way these fluxes feedback on the mean flow. While there is no clear evidence that eddies locally flux momentum into the
eastward jets of the Gulf Stream and Kuroshio extensions, a clearer picture emerges after zonally integrating across each
of the North Atlantic and North Pacific basins. We argue that the eddy momentum fluxes do indeed drive significant transport,
a conclusion supported by preliminary results from a 3-D model calculation. We also present evidence that in the North Pacific,
the Reynolds stresses are important for driving the recirculation gyres associated with the Kuroshio extension, taking advantage
of new data from both observations and high-resolution model simulations. 相似文献
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Justyna K. Przybysz-Jarnut Remus G. Hanea Jan-Dirk Jansen Arnold W. Heemink 《Computational Geosciences》2007,11(1):73-85
A data assimilation method was applied to estimate poorly known parameters (permeabilities) in a numerical reservoir model.
Most variational methods for data assimilation are based on the assumption that the model is perfect except for the poorly
known parameters. The representer method allows also for model errors, i.e. for uncertainties in the state variables (pressures
and saturations). The method is based on minimizing a cost functional, assuming all the errors and parameters to be multivariate
Gaussian random variables with given mean and covariances. The uncertain parameters and variables are expanded into a finite
sum of basis functions called representers, and the gradients of the cost functional are obtained with an adjoint method.
This approach gives an optimal parametrization in the sense that the final result is equal to the solution of the full inverse
problem. The method was tested on a simple one-dimensional model to simulate two-phase (oil-water) flow through a heterogeneous
reservoir. The results show that the method is able to provide an acceptable estimate of the permeability field. We used pressure
measurements from a small number of observation wells in between the injection and production wells, but the representer method
could be used equally well to assimilate data from other sources. The method appears to be a promising data assimilation tool
for applications in reservoir engineering. 相似文献
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Małgorzata P. Kaleta Remus G. Hanea Arnold W. Heemink Jan-Dirk Jansen 《Computational Geosciences》2011,15(1):135-153
Gradient-based history matching algorithms can be used to adapt the uncertain parameters in a reservoir model using production
data. They require, however, the implementation of an adjoint model to compute the gradients, which is usually an enormous
programming effort. We propose a new approach to gradient-based history matching which is based on model reduction, where
the original (nonlinear and high-order) forward model is replaced by a linear reduced-order forward model and, consequently,
the adjoint of the tangent linear approximation of the original forward model is replaced by the adjoint of a linear reduced-order
forward model. The reduced-order model is constructed with the aid of the proper orthogonal decomposition method. Due to the
linear character of the reduced model, the corresponding adjoint model is easily obtained. The gradient of the objective function
is approximated, and the minimization problem is solved in the reduced space; the procedure is iterated with the updated estimate
of the parameters if necessary. The proposed approach is adjoint-free and can be used with any reservoir simulator. The method
was evaluated for a waterflood reservoir with channelized permeability field. A comparison with an adjoint-based history matching
procedure shows that the model-reduced approach gives a comparable quality of history matches and predictions. The computational
efficiency of the model-reduced approach is lower than of an adjoint-based approach, but higher than of an approach where
the gradients are obtained with simple finite differences. 相似文献
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Reduced-order optimal control of water flooding using proper orthogonal decomposition 总被引：1，自引：0，他引：1
Jorn F. M. van Doren Renato Markovinović Jan-Dirk Jansen 《Computational Geosciences》2006,10(1):137-158
Model-based optimal control of water flooding generally involves multiple reservoir simulations, which makes it into a time-consuming
process. Furthermore, if the optimization is combined with inversion, i.e., with updating of the reservoir model using production
data, some form of regularization is required to cope with the ill-posedness of the inversion problem. A potential way to
address these issues is through the use of proper orthogonal decomposition (POD), also known as principal component analysis,
Karhunen–Loève decomposition or the method of empirical orthogonal functions. POD is a model reduction technique to generate
low-order models using ‘snapshots’ from a forward simulation with the original high-order model. In this work, we addressed
the scope to speed up optimization of water-flooding a heterogeneous reservoir with multiple injectors and producers. We used
an adjoint-based optimal control methodology that requires multiple passes of forward simulation of the reservoir model and
backward simulation of an adjoint system of equations. We developed a nested approach in which POD was first used to reduce
the state space dimensions of both the forward model and the adjoint system. After obtaining an optimized injection and production
strategy using the reduced-order system, we verified the results using the original, high-order model. If necessary, we repeated
the optimization cycle using new reduced-order systems based on snapshots from the verification run. We tested the methodology
on a reservoir model with 4050 states (2025 pressures, 2025 saturations) and an adjoint model of 4050 states (Lagrange multipliers).
We obtained reduced-order models with 20–100 states only, which produced almost identical optimized flooding strategies as
compared to those obtained using the high-order models. The maximum achieved reduction in computing time was 35%. 相似文献
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Diaz Cortés Gabriela Berenice Vuik Cornelis Jansen Jan-Dirk 《Computational Geosciences》2021,25(5):1621-1645
We explore and develop a Proper Orthogonal Decomposition (POD)-based deflation method for the solution of ill-conditioned linear systems, appearing in simulations of two-phase flow through highly heterogeneous porous media. We accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method achieving speed-ups of factors up to five. The up-front extra computational cost of the proposed method depends on the number of deflation vectors. The POD-based deflation method is tested for a particular problem and linear solver; nevertheless, it can be applied to various transient problems, and combined with multiple solvers, e.g., Krylov subspace and multigrid methods.
相似文献9.
Jan-Dirk Matthießen Richard John Greatbatch Martin Claus François Ascani Peter Brandt 《Ocean Dynamics》2017,67(12):1511-1522
Ocean circulation models do not generally exhibit equatorial deep jets (EDJs), even though EDJs are a recognised feature of the observed ocean circulation along the equator and they are thought to be important for tracer transport along the equator and even equatorial climate. EDJs are nevertheless found in nonlinear primitive equation models with idealised box geometry. Here we analyse several such model runs. We note that the variability of the zonal velocity in the model is dominated by the gravest linear equatorial basin mode for a wide range of baroclinic vertical normal modes and that the EDJs in the model are dominated by energy contained in vertical modes between 10 and 20. The emergence of the EDJs is shown to involve the linear superposition of several such neighbouring basin modes. Furthermore, the phase of these basin modes is set at the start of the model run and, in the case of the reference experiment, the same basin modes can be found in a companion experiment in which the amplitude of the forcing has been reduced by a factor of 1000. We also argue that following the spin-up, energy must be transferred between different vertical modes. This is because the model simulations are dominated by downward phase propagation following the spin-up whereas our reconstructions imply episodes of upward and downward propagation. The transfer of energy between the vertical modes is associated with a decadal modulation of the EDJs. 相似文献
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Waterflooding using closed-loop control 总被引：2，自引：0，他引：2
To fully exploit the possibilities of “smart” wells containing both measurement and control equipment, one can envision a
system where the measurements are used for frequent updating of a reservoir model, and an optimal control strategy is computed
based on this continuously updated model. We developed such a closed-loop control approach using an ensemble Kalman filter
to obtain frequent updates of a reservoir model. Based on the most recent update of the reservoir model, the optimal control
strategy is computed with the aid of an adjoint formulation. The objective is to maximize the economic value over the life
of the reservoir. We demonstrate the methodology on a simple waterflooding example using one injector and one producer, each
equipped with several individually controllable inflow control valves (ICVs). The parameters (permeabilities) and dynamic
states (pressures and saturations) of the reservoir model are updated from pressure measurements in the wells. The control
of the ICVs is rate-constrained, but the methodology is also applicable to a pressure-constrained situation. Furthermore,
the methodology is not restricted to use with “smart” wells with down-hole control, but could also be used for flooding control
with conventional wells, provided the wells are equipped with controllable chokes and with sensors for measurement of (wellhead
or down hole) pressures and total flow rates. As the ensemble Kalman filter is a Monte Carlo approach, the final results will
vary for each run. We studied the robustness of the methodology, starting from different initial ensembles. Moreover, we made
a comparison of a case with low measurement noise to one with significantly higher measurement noise. In all examples considered,
the resulting ultimate recovery was significantly higher than for the case of waterflooding using conventional wells. Furthermore,
the results obtained using closed-loop control, starting from an unknown permeability field, were almost as good as those
obtained assuming a priori knowledge of the permeability field. 相似文献
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