History Matching Using the Ensemble Kalman Filter With Multiscale Parameterization: A Field Case Study

SPE Journal ◽  
2010 ◽  
Vol 16 (02) ◽  
pp. 307-317 ◽  
Author(s):  
Yanfen Zhang ◽  
Dean S. Oliver
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Multiple Scales ◽  
Gaussian Random Fields ◽  
Rock Properties ◽  
Real Field ◽  
Production Data ◽  
Reservoir Properties ◽  
Water Cut

Summary The increased use of optimization in reservoir management has placed greater demands on the application of history matching to produce models that not only reproduce the historical production behavior but also preserve geological realism and quantify forecast uncertainty. Geological complexity and limited access to the subsurface typically result in a large uncertainty in reservoir properties and forecasts. However, there is a systematic tendency to underestimate such uncertainty, especially when rock properties are modeled using Gaussian random fields. In this paper, we address one important source of uncertainty: the uncertainty in regional trends by introducing stochastic trend coefficients. The multiscale parameters including trend coefficients and heterogeneities can be estimated using the ensemble Kalman filter (EnKF) for history matching. Multiscale heterogeneities are often important, especially in deepwater reservoirs, but are generally poorly represented in history matching. In this paper, we describe a method for representing and updating multiple scales of heterogeneity in the EnKF. We tested our method for updating these variables using production data from a deepwater field whose reservoir model has more than 200,000 unknown parameters. The match of reservoir simulator forecasts to real field data using a standard application of EnKF had not been entirely satisfactory because it was difficult to match the water cut of a main producer in the reservoir. None of the realizations of the reservoir exhibited water breakthrough using the standard parameterization method. By adding uncertainty in large-scale trends of reservoir properties, the ability to match the water cut and other production data was improved substantially. The results indicate that an improvement in the generation of the initial ensemble and in the variables describing the property fields gives an improved history match with plausible geology. The multiscale parameterization of property fields reduces the tendency to underestimate uncertainty while still providing reservoir models that match data.

A Probabilistic Collocation-Based Kalman Filter for History Matching

SPE Journal ◽  
2011 ◽  
Vol 16 (02) ◽  
pp. 294-306 ◽  
Author(s):  
Lingzao Zeng ◽  
Haibin Chang ◽  
Dongxiao Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Initial Conditions ◽  
Collocation Point ◽  
Computational Effort ◽  
Production Data ◽  
Sampling Errors ◽  
Probabilistic Collocation

Summary The ensemble Kalman filter (EnKF) has been used widely for data assimilation. Because the EnKF is a Monte Carlo-based method, a large ensemble size is required to reduce the sampling errors. In this study, a probabilistic collocation-based Kalman filter (PCKF) is developed to adjust the reservoir parameters to honor the production data. It combines the advantages of the EnKF for dynamic data assimilation and the polynomial chaos expansion (PCE) for efficient uncertainty quantification. In this approach, all the system parameters and states and the production data are approximated by the PCE. The PCE coefficients are solved with the probabilistic collocation method (PCM). Collocation realizations are constructed by choosing collocation point sets in the random space. The simulation for each collocation realization is solved forward in time independently by means of an existing deterministic solver, as in the EnKF method. In the analysis step, the needed covariance is approximated by the PCE coefficients. In this study, a square-root filter is employed to update the PCE coefficients. After the analysis, new collocation realizations are constructed. With the parameter collocation realizations as the inputs and the state collocation realizations as initial conditions, respectively, the simulations are forwarded to the next analysis step. Synthetic 2D water/oil examples are used to demonstrate the applicability of the PCKF in history matching. The results are compared with those from the EnKF on the basis of the same analysis. It is shown that the estimations provided by the PCKF are comparable to those obtained from the EnKF. The biggest improvement of the PCKF comes from the leading PCE approximation, with which the computational burden of the PCKF can be greatly reduced by means of a smaller number of simulation runs, and the PCKF outperforms the EnKF for a similar computational effort. When the correlation ratio is much smaller, the PCKF still provides estimations with a better accuracy for a small computational effort.

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.

Structural Surface Uncertainty Modeling and Updating Using the Ensemble Kalman Filter

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 1062-1076 ◽  
Author(s):  
A.. Seiler ◽  
S.I.. I. Aanonsen ◽  
G.. Evensen ◽  
J.C.. C. Rivenæs
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Reservoir Characterization ◽  
Production Data ◽  
Base Case ◽  
Future Production ◽  
Fixed Dimension ◽  
Structural Surface ◽  
Bottom Reservoir

Summary Although typically large uncertainties are associated with reservoir structure, the reservoir geometry is usually fixed to a single interpretation in history-matching workflows, and focus is on the estimation of geological properties such as facies location, porosity, and permeability fields. Structural uncertainties can have significant effects on the bulk reservoir volume, well planning, and predictions of future production. In this paper, we consider an integrated reservoir-characterization workflow for structural-uncertainty assessment and continuous updating of the structural reservoir model by assimilation of production data. We address some of the challenges linked to structural-surface updating with the ensemble Kalman filter (EnKF). An ensemble of reservoir models, expressing explicitly the uncertainty resulting from seismic interpretation and time-to-depth conversion, is created. The top and bottom reservoir-horizon uncertainties are considered as a parameter for assisted history matching and are updated by sequential assimilation of production data using the EnKF. To avoid modifications in the grid architecture and thus to ensure a fixed dimension of the state vector, an elastic-grid approach is proposed. The geometry of a base-case simulation grid is deformed to match the realizations of the top and bottom reservoir horizons. The method is applied to a synthetic example, and promising results are obtained. The result is an ensemble of history-matched structural models with reduced and quantified uncertainty. The updated ensemble of structures provides a more reliable characterization of the reservoir architecture and a better estimate of the field oil in place.

The Role of Geomechanical Observation in Continuous Updating of Thermal-Recovery Simulations With the Ensemble Kalman Filter

SPE Journal ◽  
2013 ◽  
Vol 18 (06) ◽  
pp. 1043-1056 ◽  
Author(s):  
A.. Azad ◽  
R.J.. J. Chalaturnyk
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Numerical Models ◽  
Thermal Recovery ◽  
Rock Properties ◽  
Observation Data ◽  
Oil Sand ◽  
Thermal Methods ◽  
Cyclic Steam Stimulation

Summary In-situ thermal methods such as steam-assisted gravity drainage (SAGD) and cyclic steam stimulation (CSS) are widely used in oil-sand reservoirs. The physics of such thermal processes is generally well-understood, and it has been shown that rock properties are highly influenced by the geomechanical behavior of the reservoir during these recovery processes. Geomechanics improves the process dynamically, and its response can depict the progress of production within a reservoir. However, the potential of geomechanical monitoring is not usually practiced. With increased implementation of highly instrumented wells and communication technologies providing real-time monitoring data from different sources, combining available data into reservoir geomechanical simulations can improve updating numerical models and the prediction process. This research explores effective uses of geomechanical observation data for history matching and types of geomechanical observation sources adequate for thermal recovery. The ensemble Kalman filter (EnKF), combined with an iterative geomechanical coupled simulator, has been chosen as the data-assimilation algorithm to update the model continuously on the basis of geomechanical observations and production data. The results show that considering geomechanical modeling and observation improves history matching when geomechanical behavior plays a role in the process.

Importance of Distributed Temperature Sensor Data for Steam Assisted Gravity Drainage Reservoir Characterization and History Matching Within Ensemble Kalman Filter Framework

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Amit Panwar ◽  
Japan J. Trivedi ◽  
Siavash Nejadi
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Reservoir Characterization ◽  
Temperature Data ◽  
Gravity Drainage ◽  
Production Data ◽  
Facies Distribution ◽  
Steam Assisted Gravity Drainage ◽  
Temperature Observations

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.

Data Assimilation Using the Constrained Ensemble Kalman Filter

SPE Journal ◽  
2010 ◽  
Vol 16 (02) ◽  
pp. 331-342 ◽  
Author(s):  
Hemant A. Phale ◽  
Dean S. Oliver
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Model Parameters ◽  
State Variables ◽  
Reservoir Properties ◽  
Compositional Model ◽  
Highly Nonlinear ◽  
Nonnegativity Constraints

Summary When the ensemble Kalman filter (EnKF) is used for history matching, the resulting updates to reservoir properties sometimes exceed physical bounds, especially when the problem is highly nonlinear. Problems of this type are often encountered during history matching compositional models using the EnKF. In this paper, we illustrate the problem using an example in which the updated molar density of CO2 in some regions is observed to take negative values while molar densities of the remaining components are increased. Standard truncation schemes avoid negative values of molar densities but do not address the problem of increased molar densities of other components. The results can include a spurious increase in reservoir pressure with a subsequent inability to maintain injection. In this paper, we present a method for constrained EnKF (CEnKF), which takes into account the physical constraints on the plausible values of state variables during data assimilation. In the proposed method, inequality constraints are converted to a small number of equality constraints, which are used as virtual observations for calibrating the model parameters within plausible ranges. The CEnKF method is tested on a 2D compositional model and on a highly heterogeneous three-phase-flow reservoir model. The effect of the constraints on mass conservation is illustrated using a 1D Buckley-Leverett flow example. Results show that the CEnKF technique is able to enforce the nonnegativity constraints on molar densities and the bound constraints on saturations (all phase saturations must be between 0 and 1) and achieve a better estimation of reservoir properties than is obtained using only truncation with the EnKF.

Global-Search Distributed-Gauss-Newton Optimization Method and Its Integration With the Randomized-Maximum-Likelihood Method for Uncertainty Quantification of Reservoir Performance

SPE Journal ◽  
2018 ◽  
Vol 23 (05) ◽  
pp. 1496-1517 ◽  
Author(s):  
Chaohui Chen ◽  
Guohua Gao ◽  
Ruijian Li ◽  
Richard Cao ◽  
Tianhong Chen ◽  
...  
Keyword(s):  
History Matching ◽  
Optimization Method ◽  
Global Search ◽  
Real Field ◽  
Production Data ◽  
Finite Difference Approximations ◽  
Production Forecasting ◽  
Novel Method ◽  
Randomized Maximum Likelihood ◽  
Search Capability

Summary Although it is possible to apply traditional optimization algorithms together with the randomized-maximum-likelihood (RML) method to generate multiple conditional realizations, the computation cost is high. This paper presents a novel method to enhance the global-search capability of the distributed-Gauss-Newton (DGN) optimization method and integrates it with the RML method to generate multiple realizations conditioned to production data synchronously. RML generates samples from an approximate posterior by minimizing a large ensemble of perturbed objective functions in which the observed data and prior mean values of uncertain model parameters have been perturbed with Gaussian noise. Rather than performing these minimizations in isolation using large sets of simulations to evaluate the finite-difference approximations of the gradients used to optimize each perturbed realization, we use a concurrent implementation in which simulation results are shared among different minimization tasks whenever these results are helping to converge to the global minimum of a specific minimization task. To improve sharing of results, we relax the accuracy of the finite-difference approximations for the gradients with more widely spaced simulation results. To avoid trapping in local optima, a novel method to enhance the global-search capability of the DGN algorithm is developed and integrated seamlessly with the RML formulation. In this way, we can improve the quality of RML conditional realizations that sample the approximate posterior. The proposed work flow is first validated with a toy problem and then applied to a real-field unconventional asset. Numerical results indicate that the new method is very efficient compared with traditional methods. Hundreds of data-conditioned realizations can be generated in parallel within 20 to 40 iterations. The computational cost (central-processing-unit usage) is reduced significantly compared with the traditional RML approach. The real-field case studies involve a history-matching study to generate history-matched realizations with the proposed method and an uncertainty quantification of production forecasting using those conditioned models. All conditioned models generate production forecasts that are consistent with real-production data in both the history-matching period and the blind-test period. Therefore, the new approach can enhance the confidence level of the estimated-ultimate-recovery (EUR) assessment using production-forecasting results generated from all conditional realizations, resulting in significant business impact.

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