Kyungbook Lee

Improvement of ensemble smoother with clustered covariance for channelized reservoirs

Ensemble Kalman filter (EnKF) has been researched for reservoir characterization in petroleum engineering. However, the repeated assimilation causes lots of simulation cost. Ensemble smoother (ES) assimilates all available data once. It has advantages over EnKF: efficiency and simplicity. The two ensemble methods are based on the same assumptions: Gaussian distribution and trust in the mean of all ensembles. Many researchers have pointed out that EnKF gives overshooting and filter divergence problems when the two key assumptions are not satisfied. This paper presents characterization of channel fields using ES with the concept of clustered covariance, especially improper ensemble design. The standard EnKF, ES, and the proposed method are applied to a 2D synthetic channel field with 200 ensembles. From distance-based clustering method, we separate initial ensembles into 10 groups based its on similarity. The proposed method uses 10 Kalman gains, since each cluster has own Kalman gain. They can represent ensembles properly by using similar ensembles instead of 200 different ensembles. For the channel fields, the standard EnKF and ES show overshooting and filter divergence problems. Updated permeability fields have extreme values and lose the continuity of channel stream. However, the proposed method manages those two problems and provides reasonable results. We can get future prediction with reliable uncertainty. The proposed method only requires about 5% of simulation time compared to EnKF, since it is based on ES. It can be applied to the characterization of channel fields, even though we have improper ensembles due to limited information.

Characterization of channelized reservoir using ensemble Kalman Filter with clustered covariance

Ensemble Kalman filter (EnKF) has the limitation of applications for multi-point geostatistics because it assumes Gaussian random field. It also uses all ensembles to get covariance matrix, even though they have different permeability field each other, resulting in filter divergence. The proposed method suggests the concept of clustered covariance by grouping initial ensembles using a distance-based method. Hausdorff distance is used for calculating similarity between permeability fields and they are separated by k-means clustering. When EnKF is applied to a 2D channel field, it shows overshooting problem and mismatches the true production data. The proposed method gives better history matching and future performance prediction without overshooting problems. Furthermore, it shows stable results for sensitivity analyses over the number of total ensembles. The more accurate covariance is calculated by clustering, the better results are obtained.

Uncertainty Quantification of Channelized Reservoir Using Ensemble Smoother with Selective Measurement Data

Ensemble smoother (ES) assimilates all available dynamic data without iterations as global update. Therefore, ES is much faster than ensemble Kalman filter (EnKF), which uses recursive updates. Iterative concepts are introduced for ES to increase accuracy of history matching. However, they lose advantages of simulation time and cost over EnKF. We propose ES with selective use of observation data in assimilation to improve history matching results and to keep simulation time short. Three methods, EnKF with all data, ES with all data, and the proposed, are applied to 2D synthetic channelized reservoirs with a nine spot waterflooding. Ensemble-based methods interpret the reason of reduced oil production rate after water breakthrough as low permeability. In this research, we suggest selective measurement data to manage misinterpretable data for the ensemble-based methods. As a logical choice, oil production rate before water breakthrough and water cut after water breakthrough are used for assimilation. EnKF with all data cannot predict true performances of oil and water productions on each well. ES with all data shows severe overshooting and filter divergence problems, which are two typical problems in the ensemble-based methods. However, the proposed method overcomes the two problems and shows good history matching results. It provides reliable uncertainty quantification of reservoir performances for both each well production and field total productions. Simulation cost of the proposed method is about 2.2% of that of EnKF, which uses 45 times update. It has clear advantage over EnKF or iterative ES methods.

History matching of channel reservoirs using ensemble Kalman filter with continuous update of channel information

Ensemble Kalman filter (EnKF) has been widely studied due to its excellent recursive data processing, dependable uncertainty quantification, and real-time update. However, many previous works have shown poor characterization results on channel reservoirs with non-Gaussian permeability distribution, which do not satisfy the Gaussian assumption of EnKF algorithm. To meet the assumption, normal score transformation can be applied to ensemble parameters. Even though this preserves initial permeability distribution of ensembles, it cannot provide reliable results when initial reservoir models are quite different from the reference one. In this study, an ensemble-based history matching scheme is suggested for channel reservoirs using EnKF with continuous update of channel information. We define channel information which consists of the facies ratio and the mean permeability of each rock face. These are added to the ensemble state vector of EnKF and updated recursively with other model parameters. Using the updated channel information, ensemble parameters are retransformed after each assimilation step. The proposed method gives better characterization results in case of using even poorly designed initial ensemble members. The method also alleviates overshooting problem of EnKF without further modifications of EnKF algorithm. The methodology is applied to channel reservoirs with extreme non-Gaussian permeability distribution. The result shows that the updated models can find channel pattern successfully and the uncertainty range is decreased properly to make a reasonable decision. Although initial channel information of the ensemble members shows big difference with the real one, it can be updated to follow the reference.

Characterization of channel oil reservoirs with an aquifer using EnKF, DCT, and PFR:

Reservoir characterization is necessary for making reliable models to have future reservoir performances. Since an aquifer typically has positive influences on oil production, its characterization has rarely been regarded as a critical issue. However, in channel oil reservoirs, an aquifer amplifies uncertainty of permeability estimations and has its own uncertainty due to limited information without any direct measurement. Although there have been some researches on channel oil reservoirs using discrete cosine transformation, we cannot characterize reliably an aquifer using discrete cosine transformation alone. Thus, we need additional schemes to manage increased uncertainty by an aquifer and to estimate the aquifer itself. In this study, ensemble Kalman filter with the combination of preservation of facies ratio and discrete cosine transformation is proposed for channel reservoirs with an aquifer. By the proposed method, we confirm that discrete cosine transformation and preservation of facies ratio contribute to preservation of overall channel properties and fine-tuning of the channel in the ensemble Kalman filter algorithm, respectively. Consequently, the proposed method gives us stable characterization performances on oil and water productions, permeability distribution, and aquifer strengths for a reasonable decision.

Improvement of Ensemble Kalman Filter for Improper Initial Ensembles

ABSTRACT Ensemble Kalman filter(EnKF) has been widely researched in petroleum industry due to uncertainty analyses and convenience to couple with commercial simulators. However, the EnKF has shown overshooting and filter divergence problems when ensemble size becomes smaller or initial ensembles are quite different from the true. These problems of the EnKF result from unified covariance between model parameters and dynamic variables. Since all ensemble members have different model parameters, especially initial ensembles are improper, it is difficult to calculate representative covariance. We introduce the concept of clustered covariance into the standard EnKF. On the assimilation step, each ensemble members can be updated using more appropriate Kalman gain rather than the unified one. From the comparison of the performances using a 2-dimensional synthetic reservoir model, the EnKF shows that root mean square (RMS) error of the logarithm of permeability increases as ensemble size becomes smaller. Furthermore, it cannot estimate the uncertainty due to incorrect dynamic prediction. It is also fluctuating with an increasing trend when assimilation time interval becomes longer. The proposed method overcomes the typical problems mentioned. It is insensitive to ensemble size and assimilation time interval, even for improper initial ensemble design cases. The RMS error is below 1 over all the cases examined including 50 ensemble size case and 100 days of assimilation time interval case. The dynamic prediction in small ensemble size is reliable with covering true performance trend despite the prediction band of initial ensemble member is failed to do so.

Estimation of soil moisture content from L- and P-band AirSAR data: A case study in Jeju, Korea

One of the important applications of polarimetric SAR in the geohydrology and agriculture is the estimation of surface soil moisture from the polarimetric SAR data. During the PacRim AirSAR campaign in Korea, the ground truth data about soil moisture content and surface roughness characteristics were collected. We intend to retrieve the surface parameters over the bare soil from multi-polarization and multi-frequency AirSAR data. In this study, the theoretical scattering model, the IEM model is inverted by two existing algorithms—the multi-dimensional regression technique by Dawson et al. (1997) and the inversion using 3-layer artificial neural networks (ANNs) (Fung, 1994). As the first step, backscatter coefficients are calculated based on the ground truth information, and then training patterns are generated from within the valid ranges of surface parameters using the IEM model. The trained inversion models are tested to a set of AirSAR data as well as synthetic data. Root mean square (RMS) errors of estimated soil moisture from the AirSAR data are average 3.1% in the regression and 4.2% in the inversion using the ANNs. The methods to improve the inversion accuracy are investigated. First, the normalization of signal parameters reduced the number of pixels that fail to reasonable results in the regression model. Second, the use of co-polarization ratio as input units in the ANNs inversion scheme improve the soil moisture estimation, which results in an average RMS error of 2.9%.

Development of fluid flow and heat transfer model in naturally fractured geothermal reservoir with discrete fracture network method

Natural fractures have a significant effect on fluid flow and heat transfer in naturally fractured geothermal reservoirs. However, most previous studies have assumed that reservoir systems are either a single continuum or dual continuum model, while some studies have just considered a pipeline model. In this study, we developed a discrete fracture network (DFN) geothermal reservoir simulator. The DFN model developed was validated for synthetic fracture systems using a Tetrad; a comparison of the results revealed good agreement between two models. However, developed model is only a fracture model and cannot simulate fluid flow and heat transfer in the matrix. A matrix flow model will be added in the future.

Iterative static modeling of channelized reservoirs using history-matched facies probability data and rejection of training image

Most inverse reservoir modeling techniques require many forward simulations, and the posterior models cannot preserve geological features of prior models. This study proposes an iterative static modeling approach that utilizes dynamic data for rejecting an unsuitable training image (TI) among a set of TI candidates and for synthesizing history-matched pseudo-soft data. The proposed method is applied to two cases of channelized reservoirs, which have uncertainty in channel geometry such as direction, amplitude, and width. Distance-based clustering is applied to the initial models in total to select the qualified models efficiently. The mean of the qualified models is employed as a history-matched facies probability map in the next iteration of static models. Also, the most plausible TI is determined among TI candidates by rejecting other TIs during the iteration. The posterior models of the proposed method outperform updated models of ensemble Kalman filter (EnKF) and ensemble smoother (ES) because they describe the true facies connectivity with bimodal distribution and predict oil and water production with a reasonable range of uncertainty. In terms of simulation time, it requires 30 times of forward simulation in history matching, while the EnKF and ES need 9000 times and 200 times, respectively.

Integration of an Iterative Update of Sparse Geologic Dictionaries with ES-MDA for History Matching of Channelized Reservoirs

This study couples an iterative sparse coding in a transformed space with an ensemble smoother with multiple data assimilation (ES-MDA) for providing a set of geologically plausible models that preserve the non-Gaussian distribution of lithofacies in a channelized reservoir. Discrete cosine transform (DCT) of sand-shale facies is followed by the repetition of K-singular value decomposition (K-SVD) in order to construct sparse geologic dictionaries that archive geologic features of the channelized reservoir such as pattern and continuity. Integration of ES-MDA, DCT, and K-SVD is conducted in a complementary way as the initially static dictionaries are updated with dynamic data in each assimilation of ES-MDA. This update of dictionaries allows the coupled algorithm to yield an ensemble well conditioned to static and dynamic data at affordable computational costs. Applications of the proposed algorithm to history matching of two channelized gas reservoirs show that the hybridization of DCT and iterative K-SVD enhances the matching performance of gas rate, water rate, bottomhole pressure, and channel properties with geological plausibility.