Error subspace filtering for atmospheric chemistry data assimilation modeling

Abstract not availableElectrical Engineering, Mathematics and Computer Scienc

A case study of the history matching of a sector of the nome field using the ensemble Kalman filter

In the history matching process reservoir parameters are estimated so they can be further used in a simulator to reproduce the past behaviour of the reservoir. During the last two decades the methodology evolved from manual methods to computer assisted procedures which can handle larger amounts of data. Now, when the computational power has increased enough, it is possible to perform more complicated computations and use more advance methods and at the same time choose more realistic simulation models. In spite of that, the field cases which are chosen to history match, even if more realistic they often are still synthetic. Therefore, the history matching procedure has been applied as a real case study based on Nome Field located near the Norwegian coastline. The preliminary results and the experience of handling realistic dataset are shared in this paper. The Ensemble Kalman Filter, which is recently a very popular method, has been chosen to match the well production rates and bottom-hole pressures to the real observations acquired in the segment of the field. Within the numerical experiment, permeability and porosity were estimated. Obtained results are a basis for continuation and the further improvement of the history matching process of the Nome Field. In addition, the issues encountered during the study are discussed i.e. the treatment of the flow conditions on the segment boundary and construction of initial ensemble. Copyright 2011, Society of Petroleum Engineers

An iterative ensemble Kalman filter for reservoir engineering applications

The study has been focused on examining the usage and the applicability of ensemble Kalman filtering techniques to the history matching procedures. The ensemble Kalman filter (EnKF) is often applied nowadays to solving such a problem. Meanwhile, traditional EnKF requires assumption of the distribution's normality. Besides, it is based on the linear update of the analysis equations. These facts may cause problems when filter is used in reservoir applications and result in sampling error. The situation becomes more problematic if the a priori information on the reservoir structure is poor and initial guess about the, e.g., permeability field is far from the actual one. The above circumstance explains a reason to perform some further research concerned with analyzing specific modification of the EnKF-based approach, namely, the iterative EnKF (IEnKF) scheme, which allows restarting the procedure with a new initial guess that is closer to the actual solution and, hence, requires less improvement by the algorithm while providing better estimation of the parameters. The paper presents some examples for which the IEnKF algorithm works better than traditional EnKF. The algorithms are compared while estimating the permeability field in relation to the two-phase, two-dimensional fluid flow model. © The Author(s) 2008

Model-reduced Variational Data Assimilation for Reservoir Model Updating

Variational data assimilation techniques (automatic history matching) can be used to adapt a prior permeability field in a reservoir model using production data. Classical variational data assimilation requires, however, the implementation of an adjoint model, which is an enormous programming effort. Moreover, it requires the results of one complete simulation of forward and adjoint models to be stored, which is a serious problem in real-life applications. Therefore, we propose a new approach to variational data assimilation that is based on model reduction, where the adjoint of the tangent linear approximation of the original model is replaced by the adjoint of a linear reduced model. The Proper Orthogonal Decomposition approach is used to determine a reduced model. Using the reduced adjoint the gradient of the objective function is approximated and the minimization problem is solved in the reduced space. If necessary, the procedure is iterated with the updated estimate of the parameters. We evaluated the model-reduced method for a simple 2D reservoir model. We compared the method with variational data assimilation where the gradient is approximated by finite differences and we found that the reduced-order method is about 50 % more efficient. We foresee that the computational efficiency will significantly increase for larger model size and our current research is focused on quantifying this computational benefit

Hydrocarbon production and reservoir management: recent advances in closed-loop optimization technology

Petroleum production is a relatively inefficient process. For oil production, it is, generally, less than 60 % effective on a macro scale and less than 60 % effective on a micro scale. This results, commonly, in an actual oil recovery of less than 35 %. Optimization of the production process will, therefore, have a significant impact on the supply of energy. At various locations in the world consortia have been set up to develop new technology that would help optimize the production process. In 2005 Shell, Delft University of Technology, and Netherlands Organization for Applied Research TNO have started the ISAPP knowledge centre. ISAPP aims to develop innovative solutions for petroleum production based on a closed loop integrated systems approach. The projects in ISAPP address both reservoir characterization issues and control issues. Apart from a short overview, this paper presents two cases from the ISAPP project portfolio: An optimal control example that shows how well head choke control can be used to prevent wax deposition during production; a reservoir characterization example that deals with production history matching and prediction of production from new wells

Data assimilation of ground-level ozone in Europe with a Kalman filter and chemistry transport model

Electrical Engineering, Mathematics and Computer Scienc

History matching using a multiscale Ensemble Kalman Filter

Since the first version of Kalman Filter was introduced in 1960 it received a lot of attention in mathematical and engineering world. There are many successful successors like for example Ensemble Kalman Filter (Evensen 1996) which has been applied also for reservoir engineering problems. The method proposed in [Zhou et al. 2007] draws together the ensemble filtering ideas and an efficient covariance representation, and is expected to perform well in history matching for reservoir engineering. It is the Ensemble Multiscale Filter. The EnMSF is a different way to represent the covariance of an ensemble. The computations are done on a tree structure and are based on an ensemble of possible realizations of the states and/or parameters of interest. The ensemble consists of replicates that are the values of states per pixel. The pixels in the grid are partitioned between the nodes of the finest scale in the tree. A construction of the tree is led by the eigenvalue decomposition. Then, the state combinations with the greatest corresponding eigenvalues are kept on the higher scales. The updated states/parameters using the EnMSF are believed to keep geological structure due to localization property. It comes from the filter s characterization where the pixels from the grid (e.g. permeability field) are distributed (in groups) over the finest scale tree nodes. We present a comparison of covariance matrices obtained with different setups used in the EnMSF. This sensitivity study is necessary since there are many parameters in the algorithm which can be adjusted to the needs of an application; they are connected to the tree construction part. The study gives the idea of how to efficiently use the EnMSF. The localization property is discussed based on the example where the filter is run with a simple simulator (2D, 2 phase) and a binary ensemble is used (the pixels in the replicates of permeability have two values only). Several possible patterns for ordering the pixels are applied

Well trajectory optimization constrained to structural uncertainties

A key objective in any reservoir development plan is to achieve maximum reservoir exploitation which is usually quantified using an economic objective such as net present value (NPV). A key element of such an optimized development plan is an optimized well planning scheme (number, placement and trajectories of the wells). In the well planning phase, it is important to quantify the geological uncertainty. In this study, a new approach is presented in which the targets and thereby the trajectories of the wells are optimized while the geological uncertainties are taken into account. The latter is achieved by using an ensemble of updated reservoir models resulting from assisted history matching (AHM) as the input for the optimization of the field development plan. For the case presented in this study, the reservoir structure, more specific the top and bottom of the reservoir, is assumed to be the main source of uncertainty. To optimize the well targets and trajectories, the Stochastic Simplex Approximate Gradients (StoSAG) methodology is used. A parameterization of the well path is proposed, in which the angles, azimuths and measured depths of the targets are used as controls to optimize the trajectories of the horizontal wells. With this parameterization, the horizontal section is not always straight, in contrast to the approaches presented in many previous publications. The proposed workflow has been applied successfully on a realistic synthetic case inspired from a real field case. The results show that significant increases in objective function can be achieved when well trajectories are optimized constrained to uncertainties in the structural mode

Application of the representer method for parameter estimation in numerical reservoir models

Applied Science