Use of Phase Streamlines for Covariance Localization in Ensemble Kalman Filter for Three-Phase History Matching

2011 ◽  
Author(s):  
Shingo Watanabe ◽  
Akhil Datta-Gupta
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Three Phase

Use of Phase Streamlines for Covariance Localization in Ensemble Kalman Filter for Three-Phase History Matching

2012 ◽  
Vol 15 (03) ◽  
pp. 273-289 ◽  
Author(s):  
Shingo Watanabe ◽  
Akhil Datta-Gupta
Keyword(s):  
Kalman Filter ◽  
Gas Phase ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Model Parameters ◽  
Ensemble Size ◽  
Three Phase ◽  
Cross Covariance ◽  
The Cross ◽  
Water Cut

Summary The ensemble Kalman filter (EnKF) has gained increased popularity for history matching and continuous reservoir-model updating. It is a sequential Monte Carlo approach that works with an ensemble of reservoir models. Specifically, the method uses cross covariance between measurements and model parameters estimated from the ensemble. For practical field applications, the ensemble size needs to be kept small for computational efficiency. However, this leads to poor approximations of the cross covariance and can cause loss of geologic realism from unrealistic model updates outside the region of the data influence and/or loss of variance leading to ensemble collapse. A common approach to remedy the situation is to limit the influence of the data through covariance localization. In this paper, we show that for three-phase-flow conditions, the region of covariance localization strongly depends on the underlying flow dynamics as well as on the particular data type that is being assimilated, for example, water cut or gas/oil ratio (GOR). This makes the traditional distance-based localizations suboptimal and, often, ineffective. Instead, we propose the use of water- and gas-phase streamlines as a means for covariance localization for water-cut- and GOR-data assimilation. The phase streamlines can be computed on the basis of individual-phase velocities which are readily available after flow simulation. Unlike the total velocity streamlines, phase streamlines can be discontinuous. We show that the discontinuities in water-phase and gas-phase streamlines naturally define the region of influence for water-cut and GOR data and provide a flow-relevant covariance localization during EnKF updating. We first demonstrate the validity of the proposed localization approach using a waterflood example in a quarter-five-spot pattern. Specifically, we compare the phase streamline trajectories with cross-covariance maps computed using an ensemble size of 2,000 for both water-cut and GOR data. The results show a close correspondence between the time evolution of phase streamlines and the cross-covariance maps of water-cut and GOR data. A benchmark uncertainty quantification (the PUNQ-S3) (Carter 2007) model application shows that our proposed localization outperforms the distance-based localization method. The updated models show improved forecasts while preserving geologic realism.

scholarly journals Parallel Implementation of the Deterministic Ensemble Kalman Filter for Reservoir History Matching

Processes ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1980
Author(s):  
Lihua Shen ◽  
Hui Liu ◽  
Zhangxin Chen
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Message Passing ◽  
History Matching ◽  
Message Passing Interface ◽  
Parallel Implementation ◽  
Computational Time ◽  
Ensemble Size ◽  
Three Phase ◽  
Reservoir History Matching

In this paper, the deterministic ensemble Kalman filter is implemented with a parallel technique of the message passing interface based on our in-house black oil simulator. The implementation is separated into two cases: (1) the ensemble size is greater than the processor number and (2) the ensemble size is smaller than or equal to the processor number. Numerical experiments for estimations of three-phase relative permeabilities represented by power-law models with both known endpoints and unknown endpoints are presented. It is shown that with known endpoints, good estimations can be obtained. With unknown endpoints, good estimations can still be obtained using more observations and a larger ensemble size. Computational time is reported to show that the run time is greatly reduced with more CPU cores. The MPI speedup is over 70% for a small ensemble size and 77% for a large ensemble size with up to 640 CPU cores.

Constructing Three-Phase Capillary Pressure Functions by Parameter Matching Using a Modified Ensemble Kalman Filter

2009 ◽  
pp. 24-48 ◽  
Author(s):  
Randi Holm ◽  
Roland Kaufmann ◽  
Elisabeth Iren Dale ◽  
Sigurd Aanonsen ◽  
Gunnar E. Fladmark ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Capillary Pressure ◽  
Ensemble Kalman Filter ◽  
Three Phase ◽  
Parameter Matching

History Matching Using the Ensemble Kalman Filter on a North Sea Field Case

2006 ◽  
Author(s):  
Vibeke Eilen Jensen Haugen ◽  
Lars-Jorgen Natvik ◽  
Geir Evensen ◽  
Aina Margrethe Berg ◽  
Kristin Margrethe Flornes ◽  
...  
Keyword(s):  
Kalman Filter ◽  
North Sea ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Field Case
Sign in / Sign up

Export Citation Format

Share Document