Browsing by Subject "Ensemble Kalman Filter"
Now showing 1 - 7 of 7
Results Per Page
Sort Options
Item A Hybrid Ensemble Kalman Filter for Nonlinear Dynamics(2011-02-22) Watanabe, ShingoIn this thesis, we propose two novel approaches for hybrid Ensemble Kalman Filter (EnKF) to overcome limitations of the traditional EnKF. The first approach is to swap the ensemble mean for the ensemble mode estimation to improve the covariance calculation in EnKF. The second approach is a coarse scale permeability constraint while updating in EnKF. Both hybrid EnKF approaches are coupled with the streamline based Generalized Travel Time Inversion (GTTI) algorithm for periodic updating of the mean of the ensemble and to sequentially update the ensemble in a hybrid fashion. Through the development of the hybrid EnKF algorithm, the characteristics of the EnKF are also investigated. We found that the limits of the updated values constrain the assimilation results significantly and it is important to assess the measurement error variance to have a proper balance between preserving the prior information and the observation data misfit. Overshooting problems can be mitigated with the streamline based covariance localizations and normal score transformation of the parameters to support the Gaussian error statistics. The swapping mean and mode estimation approach can give us a better matching of the data as long as the mode solution of the inversion process is satisfactory in terms of matching the observation trajectory. The coarse scale permeability constrained hybrid approach gives us better parameter estimation in terms of capturing the main trend of the permeability field and each ensemble member is driven to the posterior mode solution from the inversion process. However the WWCT responses and pressure responses need to be captured through the inversion process to generate physically plausible coarse scale permeability data to constrain hybrid EnKF updating. Uncertainty quantification methods for EnKF were developed to verify the performance of the proposed hybrid EnKF compared to the traditional EnKF. The results show better assimilation quality through a sequence of updating and a stable solution is demonstrated. The potential of the proposed hybrid approaches are promising through the synthetic examples and a field scale application.Item Application of the Ensemble Kalman Filter to Estimate Fracture Parameters in Unconventional Horizontal Wells by Downhole Temperature Measurements(2013-07-23) Gonzales, Sergio EduardoThe increase in energy demand throughout the world has forced the oil industry to develop and expand on current technologies to optimize well productivity. Distributed temperature sensing has become a current and fairly inexpensive way to monitor performance in hydraulic fractured wells in real time by the aid of fiber optic. However, no applications have yet been attempted to describe or estimate the fracture parameters using distributed temperature sensing as the observation parameter. The Ensemble Kalman Filter, a recursive filter, has proved to be an effective tool in the application of inverse problems to determine parameters of non-linear models. Even though large amounts of data are acquired as the information used to apply an estimation, the Ensemble Kalman Filter effectively minimizes the time of operation by only using ?snapshots? of the ensembles collected by various simulations where the estimation is updated continuously to be calibrated by comparing it to a reference model. A reservoir model using ECLIPSE is constructed that measures temperature throughout the wellbore. This model is a hybrid representation of what distributed temperature sensing measures in real-time throughout the wellbore. Reservoir and fracture parameters are selected in this model with similar properties and values to an unconventional well. However, certain parameters such as fracture width are manipulated to significantly diminish the computation time. A sensitivity study is performed for all the reservoir and fracture parameters in order to understand which parameters require more or less data to allow the Ensemble Kalman Filter to arrive to an acceptable estimation. Two fracture parameters are selected based on their low sensitivity and importance in fracture design to perform the Ensemble Kalman Filter on various simulations. Fracture permeability has very low sensitivity. However, when applying the estimation the Ensemble Kalman Filter arrives to an acceptable estimation. Similarly fracture halflength, with medium sensitivity, arrives to an acceptable estimation around the same number of integration steps. The true effectiveness of the Ensemble Kalman Filter is presented when both parameters are estimated jointly and arrive to an acceptable estimation without being computationally expensive. The effectiveness of the Ensemble Kalman Filter is directly connected to the quantity of data acquired. The more data available to run simulations, the better and faster the filter performs.Item Ensemble Statistics and Error Covariance of a Rapidly Intensifying Hurricane(2010-01-16) Rigney, Matthew C.This thesis presents an investigation of ensemble Gaussianity, the effect of non- Gaussianity on covariance structures, storm-centered data assimilation techniques, and the relationship between commonly used data assimilation variables and the underlying dynamics for the case of Hurricane Humberto. Using an Ensemble Kalman Filter (EnKF), a comparison of data assimilation results in Storm-centered and Eulerian coordinate systems is made. In addition, the extent of the non-Gaussianity of the model ensemble is investigated and quantified. The effect of this non-Gaussianity on covariance structures, which play an integral role in the EnKF data assimilation scheme, is then explored. Finally, the correlation structures calculated from a Weather Research Forecast (WRF) ensemble forecast of several state variables are investigated in order to better understand the dynamics of this rapidly intensifying cyclone. Hurricane Humberto rapidly intensified in the northwestern Gulf of Mexico from a tropical disturbance to a strong category one hurricane with 90 mph winds in 24 hours. Numerical models did not capture the intensification of Humberto well. This could be due in large part to initial condition error, which can be addressed by data assimilation schemes. Because the EnKF scheme is a linear theory developed on the assumption of the normality of the ensemble distribution, non-Gaussianity in the ensemble distribution used could affect the EnKF update. It is shown that multiple state variables do indeed show significant non-Gaussianity through an inspection of statistical moments. In addition, storm-centered data assimilation schemes present an alternative to traditional Eulerian schemes by emphasizing the centrality of the cyclone to the assimilation window. This allows for an update that is most effective in the vicinity of the storm center, which is of most concern in mesoscale events such as Humberto. Finally, the effect of non-Gaussian distributions on covariance structures is examined through data transformations of normal distributions. Various standard transformations of two Gaussian distributions are made. Skewness, kurtosis, and correlation between the two distributions are taken before and after the transformations. It can be seen that there is a relationship between a change in skewness and kurtosis and the correlation between the distributions. These effects are then taken into consideration as the dynamics contributing to the rapid intensification of Humberto are explored through correlation structures.Item Essays on Bayesian Time Series and Variable Selection(2014-05-08) De, DebkumarEstimating model parameters in dynamic model continues to be challenge. In my dissertation, we have introduced a Stochastic Approximation based parameter estimation approach under Ensemble Kalman Filter set-up. Asymptotic properties of the resultant estimates are discussed here. We have compared our proposed method to current methods via simulation studies. We have demonstrated predictive performance of our proposed method on a large spatio-temporal data. In my other topic, we presented a method for simultaneous estimation of regression parameters and the covariance matrix, developed for a nonparametric Seemingly Unrelated Regression problem. This is a very flexible modeling technique that essentially performs a sparse high-dimensional multiple predictor(p), multiple responses(q) regression where the responses may be correlated. Such data appear abundantly in the fields of genomics, finance and econometrics. We illustrate and compare performances of our proposed techniques with previous analyses using both simulated and real multivariate data arising in econometrics and government.Item Initial Member Selection and Covariance Localization Study of Ensemble Kalman Filter based Data Assimilation(2011-08-08) Yip, YeungPetroleum engineers generate reservoir simulation models to optimize production and maximize recovery. History matching is one of the methods used to calibrate the reservoir models. During traditional history matching, individual model variable parameters (permeability, relative permeability, initial water saturation, etc) are adjusted until the production history is matched using the updated reservoir model. However, this method of utilizing only one model does not help capture the full range of system uncertainty. Another drawback is that the entire model has to be matched from the initial time when matching for new observation data. Ensemble Kalman Filter (EnKF) is a data assimilation technique that has gained increasing interest in the application of petroleum history matching in recent years. The basic methodology of the EnKF consists of the forecast step and the update step. This data assimilation method utilizes a collection of state vectors, known as an ensemble, which are simulated forward in time. In other words, each ensemble member represents a reservoir model (realization). Subsequently, during the update step, the sample covariance is computed from the ensemble, while the collection of state vectors is updated using the formulations which involve this updated sample covariance. When a small ensemble size is used for a large, field-scale model, poor estimate of the covariance matrix could occur (Anderson and Anderson 1999; Devegowda and Arroyo 2006). To mitigate such problem, various covariance conditioning schemes have been proposed to improve the performance of EnKF, without the use of large ensemble sizes that require enormous computational resources. In this study, we implemented EnKF coupled with these various covariance localization schemes: Distance-based, Streamline trajectory-based, and Streamline sensitivity-based localization and Hierarchical EnKF on a synthetic reservoir field case study. We will describe the methodology of each of the covariance localization schemes with their characteristics and limitations.Item Non-Adjoint Surfactant Flood Optimization of Net Present Value and Incorporation of Optimal Solution Under Geological and Economic Uncertainty(2011-02-22) Odi, Uchenna O.The advent of smart well technology, which is the use of down hole sensors to adjust well controls (i.e. injection rate, bottomhole pressure, etc.), has allowed the possibility to control a field in all stages of the production. This possibility holds great promise in better managing enhanced oil recovery (EOR) processes, especially in terms of applying optimization techniques. However, some procedures for optimizing EOR processes are not based on the physics of the process, which may lead to erroneous results. In addition, optimization of EOR processes can be difficult, and limited, if there is no access to the simulator code for computation of the adjoints used for optimization. This research describes the development of a general procedure for designing an initial starting point for a surfactant flood optimization. The method does not rely on a simulator's adjoint computation or on external computing of adjoints for optimization. The reservoir simulator used for this research was Schlumberger's Eclipse 100, and optimization was accomplished through use of a program written in Matlab. Utility of the approach is demonstrated by using it to optimize the process net present value (NPV) of a 5-spot surfactant flood (320-acres) and incorporating the optimization solution into a probabilistic geological and economic setting. This thesis includes a general procedure for optimizing a surfactant flood and provides groundwork for optimizing other EOR techniques. This research is useful because it takes the optimal solution and calculates a probability of success for possible NPVs. This is very important when accessing risk in a business scenario, because projects that have unknown probability of success are most likely to be abandoned as uneconomic. This thesis also illustrates possible NPVs if the optimal solution was used.Item Testing a Coupled Global-limited-area Data Assimilation System Using Observations from the 2004 Pacific Typhoon Season(2012-10-19) Holt, ChristinaTropical cyclone (TC) track and intensity forecasts have improved in recent years due to increased model resolution, improved data assimilation, and the rapid increase in the number of routinely assimilated observations over oceans. The data assimilation approach that has received the most attention in recent years is Ensemble Kalman Filtering (EnKF). The most attractive feature of the EnKF is that it uses a fully flow-dependent estimate of the error statistics, which can have important benefits for the analysis of rapidly developing TCs. We implement the Local Ensemble Transform Kalman Filter algorithm, a variation of the EnKF, on a reduced-resolution version of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) model and the NCEP Regional Spectral Model (RSM) to build a coupled global-limited area analysis/forecast system. This is the first time, to our knowledge, that such a system is used for the analysis and forecast of tropical cyclones. We use data from summer 2004 to study eight tropical cyclones in the Northwest Pacific. The benchmark data sets that we use to assess the performance of our system are the NCEP Reanalysis and the NCEP Operational GFS analyses from 2004. These benchmark analyses were both obtained by the Statistical Spectral Interpolation, which was the operational data assimilation system of NCEP in 2004. The GFS Operational analysis assimilated a large number of satellite radiance observations in addition to the observations assimilated in our system. All analyses are verified against the Joint Typhoon Warning Center Best Track data set. The errors are calculated for the position and intensity of the TCs. The global component of the ensemble-based system shows improvement in position analysis over the NCEP Reanalysis, but shows no significant difference from the NCEP operational analysis for most of the storm tracks. The regional component of our system improves position analysis over all the global analyses. The intensity analyses, measured by the minimum sea level pressure, are of similar quality in all of the analyses. Regional deterministic forecasts started from our analyses are generally not significantly different from those started from the GFS operational analysis. On average, the regional experiments performed better for longer than 48 h sea level pressure forecasts, while the global forecast performed better in predicting the position for longer than 48 h.