Uncertainty Space Expansion: A Consistent Integration of Measurement Errors in Linear Inversion

Channelized reservoirs consist of sinusoid patterns for sandstone. It is the most important for decision making to characterize connectivities because they significantly affect reservoir performances. Ensemble Kalman filter (EnKF) and ensemble smoother (ES) modify reservoir models using dynamic data. However, it is difficult for them to apply to channelized reservoirs because they assume that model parameters follow Gaussian distribution. The purpose of this research is to characterize 3D channel connectivities using ensemble-based methods. We use the concept of multiple Kalman gains for improved inverse modeling and it is applied to ES for fast history matching. Multiple Kalman gains are calculated by distance-based method such as hausdorff distance and kernel kmeans clustering. The proposed method, ES with multiple Kalman gains, is compared to EnKF and ES for 3D synthetic case. It solves overshooting problem in ES and describes better channel connectivities and bimodal distribution than EnKF. Furthermore, it requires only 6.4% simulation time of EnKF. When oil production rates and water cuts are predicted by updated ensembles, only the proposed method gives reliable uncertainty quantifications while EnKF and ES deviate from the true productions. Therefore, the proposed method can be utilized for fast decision making tool for 3D channelized reservoirs.

Even though the ensemble Kalman filter (EnKF) is widely used, history matching reservoirs with facies description has proven to be a major challenge. A preferred technique for estimating large-scale facies fields within the petroleum industry is still missing. In this paper we present a new approach to this problem. Instead of applying the EnKF directly on facies realizations, the approach applies a transformation of facies fields to a specific level-set function, representing distances between facies types. This ensures better agreement with the EnKF Gaussianity assumptions, and the method always returns facies realizations with geological authenticity. The method also offers large flexibility in generating the initial ensemble, which can be done using any geostatistical tool. Further, no modifications of the standard EnKF equations are needed. The methodology is evaluated on two synthetic examples with increasing complexity. In both examples we consider reservoirs with channel structure. The results presented show that the updated models give large improvements in matching the measurements, and the uncertainty of the models is decreased. Further, recovery of the true petrophysical parameters is highly dependent on sufficient information in the measurements, but in one of the examples considered we are able to completely recover the true channel structure. Additional improvements in the quality of the updated facies fields are obtained by proper handling of the distances close to the reservoir boundaries, and conditioning on specific statistical measures to better preserve prior information about channel properties. Introduction The ensemble Kalman filter (EnKF) (Evensen [1], Aanonsen et al. [2]) is one of the most promising tools for assisted history matching of reservoir models. The filter has in particular proven to work well on cases where petrophysical properties are modeled using Gaussian random fields with variogram models. However, many operative oil and gas reservoirs have challenging complex geological structures - channelized reservoirs being one example. These structures typically have rapid spatial variations in the petrophysical properties (e.g., permeability and porosity). The effect of applying the EnKF directly on such reservoirs is that the characteristics of the fields are lost, i.e., sharp gradients are smeared out (dissipated). Several approaches for using EnKF on complex reservoirs have been proposed. The goal is to ensure that the updated fields are facies realizations, or at least approximations of such, and that good history match is obtained. The methods involve use of truncated pluri-Gaussian methods (Liu and Oliver [3, 4]), Gaussian mixture models (Dovera and Della Rossa [5], Sun et al. [6]), discrete cosine transformations (Jafarpour and McLaughlin [7]), kernel methods (Sarma and Chen [8]), and level-set methods (Moreno et al. [9]). Many of the above mentioned methods give promising results, but there are still drawbacks related to e.g., flexibility in how the initial ensemble may be generated, or the method involves complex and large modifications of the standard EnKF implementation. Our goal is to develop a methodology which is both simple, flexible and able to preserve facies structure for the updated fields. To achieve this, we propose a method motivated by the work of Moreno et al. [9], in the sense that level-set functions are used to represent the facies fields. However, in Moreno et al. [9], only perturbations of a fixed "base case" are updated, and it is questionable whether the real uncertainty is properly described by the prior ensemble. The method we propose is not limited to updating perturbations, and the initial ensemble can be computed using any geostatistical tool. This means that using our methodology, the initial ensemble can be conditioned on the correct facies types at the well locations. The method relies on a transformation of the facies field to a specific level-set function - a signed distance function (representing distances between opposite facies types). The distances are then updated using the EnKF, and converted to petrophysical properties when the reservoir simulator is run to the next assimilation time. The advantage with this transformation is that the ensemble of parameters to be estimated is closer to a Gaussian distribution, which is in better agreement with the EnKF Gaussianity assumptions. In addition, we are guaranteed that the updated fields are facies realizations.

Many recent developments in generating history matched reservoir models that approximately characterize subsurface uncertainty are associated with the ensemble smoother (ES) method. It is much better suited for practical history matching applications because it does not require updating of the dynamical variables and thus the frequent simulation restarts required by ensemble kalman filter (EnKF) are avoided. However, the performance of original single update scheme of ES is poor for strongly nonlinear problems and therefore iterations may be needed. Several iterative forms of ES were proposed in the past few years, most of which combine ideas from random maximum likelihood (RML) and ensemble-based techniques. Unlike previous implementations, we pose the history matching problem as a full nonlinear least squares optimization problem and classical Levenberg-Marquardt (LM) algorithm is used as the optimization solver. By showing the that solution of the linearized least squares subproblems arising from each iteration has similar structure to that of standard ES update equation, we propose to use ES as the linear least squares solver to avoid the expensive adjoint calculation. In this way, the proposed algorithm can be considered as an iterative ES and the regularization parameter can be updated following the standard LM rule. Furthermore, because it is casted as an optimization problem, it is straightforward to extend it to robust nonlinear least squares method that can automatically estimate the measurement noise level and reduce the effect of outliers in the data that is essential for field applications. Two synthetic reservoir models are used to showcase the effectiveness and robustness of the newly developed algorithm.

Multiple assisted history matching (AHM) techniques commonly applied in the oil and gas industry were benchmarked for their applicability to field studies. The benchmarking effort was aimed at exploration of the theoretical as well as practical benefits, challenges and tradeoffs of the AHM techniques as they are utilized for asset development and reservoir management. This paper specifically discusses benchmarking of ensemble-based methods as applied for history matching of a key deepwater asset for the corporation. Two variations of ensemble-based methods are examined: the ensemble Kalman filter (EnKF) (Evensen, 2009) and the ensemble smoother with multiple data assimilation (ES-MDA) (Emerick and Reynolds, 2013). In both techniques, the ensemble of parameter estimates evolves as field data are assimilated into the reservoir characterization, either sequentially using the EnKF or iteratively using the ES-MDA. Both of these variations have been deployed with adaptive bootstrap-based screening (Zhang and Oliver, 2011) to reduce the sampling error of ensemble estimates. One significant strength of ensemble-based methods is their ability to estimate high-resolution model parameters. In this benchmark study, however, the ensemble-based methods were applied for estimation of a group of low-resolution model parameters including regional property multipliers and pilot points. The insights gained from the inverse problem of constraining reservoir simulation models to historical production data can be particularly valuable in guiding the practitioner in re-definition of the prior model uncertainty and towards the model solution. The study shows that a major challenge in the application of ensemble-based methods is parameter over-adjustment resulting from the improper addition of observation errors associated with the actual observations. In practice, multiple experiments are required for the user to iteratively improve the optimal level of the added errors. As the number of observations grows large, the increase in computational cost and decrease in ensemble variability are additional challenges in the application of ensemble-based methods. While assimilating different types of data, a balanced proportion of these data types should be maintained. These points are illustrated and discussed in the field application section of the paper.

Time-lapse seismic data has been widely used for the detailed reservoir characterization, and data assimilation algorithms are commonly used for petroleum reservoir history matching of production data. However, hardly any seismic data has been integrated into the reservoir inverse modeling workflow, due to the large data size, finer gridding, and especially the scarcity in time of the seismic data. Popular ensemble-based reservoir inverse modeling methods such as ensemble Kalman filter (EnKF) also face the problems of high computational cost due to the storage of the intermediate variables, restarting the reservoir simulating process and the inconsistency of the full-step and step-wise simulations. The intrinsic sequential data assimilations characteristics of the EnKF set obstacles to assimilate 4D seismic data. The alternative method can be the ensemble smoother (ES), which is an ensemble based method for data assimilation. The ES is based on a Bayesian updating scheme of the reservoir model to match the production history and improve the production forecast. To improve the algorithm convergence, a multiple data assimilation (MDA) method was proposed by Emerick and Reynolds (2012a). The algorithm we used is called ensemble smoother with multiple data assimilation (ESMDA), we modified the ESMDA to integrate the geophysical data, and created the new workflow to history match both the production and geophysical data. The available production data is well measurements, including oil production rate, well water cut and bottom-hole pressure, as well as time-lapse geophysical data, including P-wave impedance. In this paper, we first formulated the mathematical descriptions of ESMDA, we then down-scaled the seismic data, and modified the data assimilation algorithms, illustrated the history matching workflow for both production and geophysical data, finally, we showed how it works with a case study on a water flooding operation in a synthetic reservoir. In comparison, we also showed the history matching only on the production data, which yields an inferior results than the one matches both production and seismic data.

This work focuses on the improvement of an integrated methodology for the automatic history matching of compartmentalised reservoirs using 4D seismic results, stochastic initialization and the Ensemble Kalman Filter method. We show the comparison of two different history matching approaches using the Ensemble Kalman Filter (EnKF) to update the Fault Transmissibility Multipliers (FTM) initially estimated with and without considering the 4D seismic results. In this study, the parameters updated during the history matching are two-phase fault transmissibility multipliers (FTM), absolute permeability and effective porosity of a synthetic realistic 3D reservoir. The true impedance map and the changes in reservoir pressure and saturation were previously computed from 4D seismic results. The systematic estimation of two-phase fault transmissibility multipliers is based on the integration of the collected 4D seismic results and an established method validated in our previous work based on a deterministic model, using the gradient-based History Matching, Levenberg Marquardt method (LM). We present the history matching of a synthetic reservoir using the Ensemble Kalman Filter (EnKF) considering the 4D seismic results to update the models and geostatistical techniques to produce the initial geological models. The stochastic method used is the Sequential Gaussian Simulation (SGS) technique to generate 100 initial models. During history matching using the EnKF, the saturation distributions are computed from the forward modelling of a two-phase system (oil-water). The impedance maps are then estimated using the Gassmann equation and compared with the true impedance map as part of the History Matching process. To validate the results, the cost function consisting of two components is calculated, the first is the structural similarity index of the two reconstructed impedance images to the real impedance image and the second is the RMS cost function value, l2 – norm of the difference between the true (real) and the simulated pressure-production data. The EnKF history matching using the two-phase FTM values considering 4D seismic results produced lower cost function values compared with the model using the initial FTM multiplier without considering 4D seismic results. The EnKF history matching algorithm using 4D seismic presented in this work produced results closer to the true reservoir impedance map compared to our previous 4D gradient based history matching method.

This paper presents the application of the ensemble Kalman filter (EnKF) method to the integration of well test data into heterogeneous reservoir models generated from geological and geophysical data. EnKF does not require computing the gradient of an objective function, and hence can be applied easily with any reservoir simulator, and more importantly, is far more efficient than a gradient-based history matching procedure when the forward model is represented by a reservoir simulator. In the procedure for integrating pressure transient data considered here, the static geological/geophysical data are assumed to be encapsulated in a multivariate probability density function characterized by a prior mean and covariance for the joint distribution of the porosity and permeability fields. As the prior mean of the property fields obtained from the core and log data can sometimes be erroneous, a partially doubly stochastic model is applied to account for the uncertainty of the prior mean. In the doubly stochastic model, a correction to the prior mean is adjusted together with the heterogeneous field during history matching. The method is tested with synthetic heterogeneous single-layer and two-layer reservoirs. Excellent data matches are obtained with EnKF in a small fraction of the time that would be required for a gradient-based history-matching process and the observed data fall within the uncertainty bounds of the ensemble data predictions. In the layered reservoir case, the uncertainty in rock property fields is further reduced by integration of production log data (layer flow rates). We show that problems of statistical inconsistency and poor data matches that are sometimes encountered when matching production data with EnKF do not occur when matching pressure data with the EnKF implementation used here. This undoubtedly occurs because the dynamical system (reservoir simulator equations) is much more nearly linear for the single-phase flow problems considered here than for multiphase flow cases.

Understanding the porosity distributions across whole reservoirs is crucial in all stages of the exploration and production, such as estimating the original oil/gas in place and recoverable resources, selecting primary/secondary recovery mechanisms, optimizing enhanced recovery methods, etc. Nevertheless, there are no direct methods to probe inter-well porosity beyond near wellbore core analysis or loggings. Here, we propose a new method to directly measure the inter-well porosity using polymeric and molecular inter-well tracers. Specifically, we utilize the transport property of polymers in porous media that the polymers can bypass small pores, i.e., the inaccessible pore volume (IPV), resulting in accelerated breakthrough. In contrast, small molecular tracers will flow through all pores without accelerated breakthrough. By comparing the breakthrough curves of the polymeric and molecular tracers, the inter-well porosity can be measured. We performed reservoir simulations to demonstrate the workflow. In the meantime, we synthesized model low-retention polymer tracer candidates and characterized their IPV in carbonate cores using coreflood experiments. In reservoir simulations, we constructed waterflooding scenarios with both polymeric and molecular water tracers co-injected into injectors and observed their breakthrough curves from producers. Depending on the different porosity distributions between injector-producer pairs, the polymeric tracers can either breakthrough much faster than the molecular tracers, or both polymeric and molecular tracers may breakthrough at a similar time. Ensemble smoother with multiple data assimilation with tracer data (ES-MDA-Tracer) algorithms were then used for history matching and predicting the inter-well porosity. Encouragingly, including both polymeric and molecular tracers resulted in much improved inter-well porosity predictions. In our experimental effort, we synthesized different sizes of the low retention sulfozwitterionic poly(1-vinylimidazole) (PZVIm) polymers that are good candidates for inter-well porosity-sensing tracers. Coreflood experiments co-injecting sulfozwitterionic PZVIm polymer tracers with reference NaBr water tracers in representative carbonate cores showed an IPV of ~10% for the polymers with molecular weight of 46,000 g/mol. Larger polymers may be synthesized to increase the IPV to have more dramatic breakthrough contrasts in the proposed filed applications. In this paper, we presented a novel approach for the direct measurement of inter-well porosity by means of the different transport properties of the polymeric and molecular inter-well tracers, which the polymers are pore-sensitive (with IPV) while the molecular tracers are pore-insensitive. Detailed workflows were demonstrated using reservoir simulations and history matching algorithms. Finally, novel candidate polymers (sulfozwitterionic PZVIm) for this application were experimentally synthesized and verified, which greatly strengthened the validity of our approach.

Recently, the Ensemble Kalman Filter (EnKF) has emerged as an effective tool for performing continuous updating of petroleum reservoir simulation models. The method is firmly grounded on the theory of Kalman filters and sequential Monte Carlo techniques. The ability of the method to sequentially update the spatial properties in petroleum reservoir models, such as permeability and porosity, by integrating the dynamic production data makes it a very attractive approach. Moreover, the method takes into account the production uncertainty in the reservoir models by using error covariance matrices for the measurement vector (Production and injection rates, Gas-Oil ratio, Steam-Oil ratio, etc.) and the state vector (pressure, saturation, permeability, porosity). Similar to the traditional Kalman filter, the covariance matrices have to be tuned to reflect the uncertainty in the model and the measurements. We consider two unconventional oil reservoir models: 1) highly heterogeneous black-oil reservoir model, and 2) heterogeneous SAGD reservoir model. The results will demonstrate the advantage of using the localized EnKF for effective history matching using ensemble sizes relatively lower than what otherwise would be required with the ordinary EnKF. The results will also show the advantages of using prior knowledge available from the wells (permeability and porosity measurements) to generate initial realizations. One of the main practical advantages of history matching using the EnKF over traditional optimization based approaches is its low computational effort. The computational cost is dominated by Monte Carlo simulation of the ensemble of models only. Thus, significant computational time saving is possible by running each of the ensemble simulations on independent processors in a parallel mode. Moreover, the method can be easily integrated with any commercial reservoir simulation software.

The Ensemble Kalman Filter (EnKF) has gained popularity over recent years as a Monte-Carlo based technique for assisted history matching and real time updating of reservoir models. The EnKF procedure utilizes an ensemble of model states (e.g. realizations of reservoir properties such as porosity and permeability) to approximate the covariance matrices used in the updating process. EnKF works efficiently with Gaussian variables and linear dynamics, but it often fails to preserve the reference probability distribution of the model parameters and to achieve an acceptable production data match where the system dynamics are strongly nonlinear, especially of the type related to multiphase flow, or if non-Gaussian prior models are used. In order to alleviate these drawbacks, we investigated various weighted averaging techniques for computing the ensemble mean by introducing a weighting factor to each ensemble; two new formulations were implemented. The first weighting factor was calculated based on the mismatch in entropy of the model parameters, a normalized measure of the spread of a given probability distribution. The second weighting factor was computed using the forecast mismatch. In addition, both weights could be applied at a single updating step for reducing the forecast mismatch and maintaining the prior distribution simultaneously. The performance of traditional EnKF and these weighted EnKF methods were evaluated by performing various simulation studies with different reservoir heterogeneity. The qualities of the final matching results were assessed by computing the experimental histogram and variograms of the final ensemble, as well as the Root Mean Square Error (RMSE) of the predicted data mismatch. The results reveal that reasonable improvement in the efficiency of the EnKF is achieved by suggested weighted techniques. The RMSE of the predicted data is improved, and the quantity of spurious model parameters is reduced at each updating step. Taking advantage of the entropy based weighting factor assists the filter to preserve the reference distribution. The improvement indicates that the Entropy weighted EnKF (EWEnKF) has a significant potential to resolve the shortfall of traditional EnKF in reservoir characterization and history matching of challenging reservoirs with non-Gaussian distributions.

Recently, the ensemble Kalman filter (EnKF) has gained popularity in atmospheric science for the assimilation of data and the assessment of uncertainty in forecasts for complex, large-scale problems. A handful of papers have discussed reservoir characterization applications of the EnKF, which can easily and quickly be coupled with any reservoir simulator. Neither adjoint code nor specific knowledge of simulator numerics is required for implementation of the EnKF. Moreover, data are assimilated (matched) as they become available; a suite of plausible reservoir models (the set of ensembles) is continuously updated to honor data without rematching data assimilated previously. Because of these features, the method is far more efficient for history matching dynamic data than automatic history matching algorithms based on optimization algorithms. Moreover, the suite of ensembles provides a way to evaluate the uncertainty in reservoir description and performance predictions. Here we establish a firm theoretical relation between randomized maximum likelihood and the ensemble Kalman filter. We also consider examples where the performance of the EnKF does not provide a reliable characterization of uncertainty in the model or performance predictions. Although we have previously generated reservoir characterization examples where the method worked well, here we also provide examples where the performance of EnKF does not provide a reliable characterization of uncertainty.

Streamline-based assisted and automatic history matching techniques have shown great potential in reconciling high resolution geologic models to production data. However, a major drawback of these approaches has been incompressibility or slight compressibility assumptions that have limited applications to two-phase water-oil displacements only. We propose an approach to history matching three-phase flow using a novel compressible streamline formulation and streamline-derived analytic sensitivities. First, we utilize a generalized streamline model to account for compressible flow by introducing an 'effective density' of total fluids along streamlines. Second, we analytically compute parameter sensitivities that define the relationship between the reservoir properties and the production response, viz. water-cut and gas/oil ratio (GOR). These sensitivities are an integral part of history matching, and streamline models permit efficient computation of these sensitivities through a single flow simulation. We calibrate geologic models to production data by matching the water-cut and gas/oil ratio using our previously proposed generalized travel time inversion (GTTI) technique. For field applications, however, the highly non-monotonic profile of the gas/oil ratio data often presents a challenge to this technique. In this work we present a transformation of the field production data that makes it more amenable to GTTI. Further, we generalize the approach to incorporate bottom-hole flowing pressure during three-phase history matching. We examine the practical feasibility of the method using a field-scale synthetic example (SPE-9 comparative study) and a field application. Recently Ensemble Kalman Filtering (EnKF) has gained increased attention for history matching and continuous reservoir model updating using data from permanent downhole sensors. It is a sequential Monte-Carlo approach that works with an ensemble of reservoir models. Specifically, the method utilizes cross-covariances 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 matrix, resulting in loss of geologic realism. Specifically, the updated parameter field tends to become scattered with a loss of connectivities of extreme values such as high permeability channels and low permeability barriers, which are of special significance during reservoir characterization. We propose a novel approach to overcome this limitation of the EnKF through a 'covariance localization' method that utilizes sensitivities that quantify the influence of model parameters on the observed data. These sensitivities are used in the EnKF to modify the cross-covariance matrix in order to reduce unwanted influences of distant observation points on model parameter updates. The key to the success of the sensitivity-based covariance-localization is its close link to the underlying physics of flow compared to a simple distance-dependent covariance function as used in the past. This flow-relevant conditioning leads to an efficient and robust approach for history matching and continuous reservoir model updating, avoiding much of the problems in traditional EnKF associated with instabilities, parameter overshoots and loss of geologic continuity. We illustrate the power and utility of our approach using both synthetic and field applications.

Distributed temperature sensing (DTS), an optical fiber down-hole monitoring technique, provides a continuous and permanent well temperature profile. In steam assisted gravity drainage (SAGD) reservoirs, the DTS plays an important role to provide depth-and-time continuous temperature measurement for steam management and production optimization. These temperature observations provide useful information for reservoir characterization and shale detection in SAGD reservoirs. However, use of these massive data for automated SAGD reservoir characterization has not been investigated. The ensemble Kalman filter (EnKF), a parameter estimation approach using these real-time temperature observations, provides a highly attractive algorithm for automatic history matching and quantitative reservoir characterization. Due to its complex geological nature, the shale barrier exhibits as a different facies in sandstone reservoirs. In such reservoirs, due to non-Gaussian distributions, the traditional EnKF underestimates the uncertainty and fails to obtain a good production data match. We implemented discrete cosine transform (DCT) to parameterize the facies labels with EnKF. Furthermore, to capture geologically meaningful and realistic facies distribution in conjunction with matching observed data, we included fiber-optic sensor temperature data. Several case studies with different facies distribution and well configurations were conducted. In order to investigate the effect of temperature observations on SAGD reservoir characterization, the number of DTS observations and their locations were varied for each study. The qualities of the history-matched models were assessed by comparing the facies maps, facies distribution, and the root mean square error (RMSE) of the predicted data mismatch. Use of temperature data in conjunction with production data demonstrated significant improvement in facies detection and reduced uncertainty for SAGD reservoirs. The RMSE of the predicted data is also improved. The results indicate that the assimilation of DTS data from nearby steam chamber location has a significant potential in significant reduction of uncertainty in steam chamber propagation and production forecast.

Most geostatistical methods for generating plausible facies models require prior knowledge of the facies proportions distribution to account for heterogeneity within the reservoir. This parameter affects the flow behavior, predictive performance and fluid volume distribution of the model. In practice, it is hardly known with certainty and it is important to account for this uncertainty in the modeling and history matching phases. The ensemble Kalman filter (EnKF), when modified appropriately, to account for non-linearity and non-Gaussianity, is quite robust for automatic history matching problems. However, because the problem of history matching applied to facies is complex, most attempts at solving this problem typically assume constant petrophysical properties and stationary facies proportions. However, realistic representation of facies distribution requires incorporating the variation in petrophysical properties in the geologic model, in addition to any associated uncertainty. This is critical to correctly defining the flow connectivity within the model and the variations in storativity within facies. In this paper, we investigate a number of practical issues in history matching applied to facies with heterogeneous petrophysical properties and non-stationary proportions: (1) Can we account for heterogeneity in facies petrophysical properties during history matching and subsequently reduce any associated uncertainty in them by sequential calibration to data? To the best of our knowledge, this is the first time that heterogeneity in facies petrophysical properties has ever been applied to problems of this kind; (2) What is the EnKF performance when the facies proportions are stationary but implicitly uncertain? (3) Can EnKF efficiently adjust the facies boundaries and distributions when the prior proportions are assumed known but non-stationary? To answer these questions we designed three different test problems. We show that when the facies proportion is non-stationary the EnKF is a robust in estimating the facies properties and distribution.

Ensemble Kalman filter (EnKF) is one of the powerful optimization schemes for production data history matching in petroleum engineering. It provides promising characterization results and dependable future prediction of production performances. However, it needs high computational cost due to its recursive updating procedures. Ensemble smoother (ES), which updates all available observation data at once, has high calculation efficiency but tends to give unreliable results compared with EnKF. Particularly, it is challenging to channel reservoirs, because geological parameters of those follow a bimodal distribution. In this paper, we propose a new ES method using a channel information update scheme and discrete cosine transform (DCT). The former can assimilate channel information of ensemble models close to the reference, maintaining a bimodal distribution of parameters. DCT is also useful for figuring out main channel features by extracting out essential coefficients which represent overall channel characteristics. The proposed method is applied to two cases of 2D and 3D channel reservoirs and compared with EnKF and ES. The method not only provides reliable characterization results with clear channel connectivity but also preserves a bimodal distribution of parameters. In addition, it gives dependable estimations of future production performances by reducing uncertainties in the prior models.