Remus G. Hanea

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

[1] A Kalman filter coupled to the atmospheric chemistry transport model EUROS has been used to estimate the ozone concentrations in the boundary layer above Europe. Two Kalman filter algorithms, the reduced rank square root (RRSQRT) and the ensemble Kalman filter (ENKF), were implemented in this study. Both required, in general, a large number of EUROS model simulations for an assimilation. The observations consisted of hourly ozone data in a set of 135 ground-based stations in Europe for the period, June 1996. Half of these stations were used for the assimilation and the other half only for validation of the results. The combination between data assimilation (Kalman filter) and the atmospheric chemistry transport model, EUROS, gave more accurate results for boundary layer ozone than the EUROS model or measurements used separately. The average difference between assimilated and measured ozone concentrations decreased from 27.4 to 20.5 m gm � 3 for the average of the stations used for validation in Europe. Both algorithms tend to converge to about the same accuracy, with an increasing number of EUROS model runs. About 10–20 EUROS model calculations were found sufficient for a good assimilation. The results are supported by a number of simulations that also reveal a local character for the assimilation process. INDEX TERMS: 3337 Meteorology and Atmospheric Dynamics: Numerical modeling and data assimilation; 3307 Meteorology and Atmospheric Dynamics: Boundary layer processes; 0345 Atmospheric Composition and Structure: Pollution—urban and regional (0305); 0368 Atmospheric Composition and Structure: Troposphere—constituent transport and chemistry; KEYWORDS: atmospheric NOx, VOC

A probabilistic parametrization for geological uncertainty estimation using the ensemble Kalman filter (EnKF)

In the past years, many applications of history-matching methods in general and ensemble Kalman filter in particular have been proposed, especially in order to estimate fields that provide uncertainty in the stochastic process defined by the dynamical system of hydrocarbon recovery. Such fields can be permeability fields or porosity fields, but can also fields defined by the rock type (facies fields). The estimation of the boundaries of the geologic facies with ensemble Kalman filter (EnKF) was made, in different papers, with the aid of Gaussian random fields, which were truncated using various schemes and introduced in a history-matching process. In this paper, we estimate, in the frame of the EnKF process, the locations of three facies types that occur into a reservoir domain, with the property that each two could have a contact. The geological simulation model is a form of the general truncated plurigaussian method. The difference with other approaches consists in how the truncation scheme is introduced and in the observation operator of the facies types at the well locations. The projection from the continuous space of the Gaussian fields into the discrete space of the facies fields is realized through in an intermediary space (space with probabilities). This space connects the observation operator of the facies types at the well locations with the geological simulation model. We will test the model using a 2D reservoir which is connected with the EnKF method as a data assimilation technique. We will use different geostatistical properties for the Gaussian fields and different levels of the uncertainty introduced in the model parameters and also in the construction of the Gaussian fields.

A Hybrid Kalman Filter Algorithm for Large-Scale Atmospheric Chemistry Data Assimilation

Abstract In the past, a number of algorithms have been introduced to solve data assimilation problems for large-scale applications. Here, several Kalman filters, coupled to the European Operational Smog (EUROS) atmospheric chemistry transport model, are used to estimate the ozone concentrations in the boundary layer above Europe. Two Kalman filter algorithms, the reduced-rank square root (RRSQRT) and the ensemble Kalman filter (EnKF), were implemented in a prior study. To combine the best features of these two filters, a hybrid filter was constructed by making use of the reduced-rank approximation of the covariance matrix as a variance reducer for the EnKF. This hybrid algorithm, complementary orthogonal subspace filter for efficient ensembles (COFFEE), is coupled to the EUROS model. The performance of all algorithms is compared in terms of residual errors and number of EUROS model evaluations. The COFFEE results score somewhere between the EnKF and RRSQRT results for less than approximately 30 model eval...

History Matching Time-Lapse Surface-Gravity and Well-Pressure Data With Ensemble Smoother for Estimating Gasfield Aquifer Support--A 3D Numerical Study

Water influx is an important factor influencing production of gas reservoirs with an active aquifer. However, aquifer properties such as size, porosity, and permeability are typically uncertain and make predictions of field performance challenging. The observed pressure decline is inherently nonunique with respect to water influx, and large uncertainties in the actual reservoir state are common. Time-lapse (4D) gravimetry, which is a direct measure of a subsurface mass redistribution, has the potential to provide valuable information in this context. Recent improvements in instrumentation and data-acquisition and -processing procedures have made time-lapse gravimetry a mature monitoring technique, both for land and offshore applications. However, despite an increasing number of gas fields in which gravimetric monitoring has been applied, little has been published on the added value of gravity data in a broader context of modern reservoir management on the basis of the closed-loop concept. The way in which gravity data can contribute to improved reservoir characterization, production-forecast accuracy, and hydrocarbon-reserves estimation is still to be addressed in many respects. In this paper, we investigate the added value of gravimetric observations for gasfield-production monitoring and aquifer-support estimation. We perform a numerical study with a realistic 3D gasfield model that contains a large and complex aquifer system. The aquifer support and other reservoir parameters (i.e., porosity, permeability, reservoir top and bottom horizons) are estimated simultaneously using the ensemble smoother (ES). We consider three cases in which gravity only is assimilated, pressure only is assimilated, and gravity and pressure data are assimilated jointly. We show that a combined estimation of the aquifer support with the permeability field, porosity field, and reservoir structure is a very challenging and nonunique history-matching problem, in which gravity certainly has an added value. Pressure data alone may not discriminate between different reservoir scenarios. Combining pressure and gravity data may help to reduce the nonuniqueness problem and provide not only an improved gas- and water-production forecast and gas-in-place evaluation, but also a more-accurate reservoir-state description

Observation Sensitivity in Computer-assisted History Matching

This study concerns computer-assisted history matching of reservoir simulation models, i.e. systematic updating of model parameters to minimize the mismatch between observed and simulated production data, with the aim to improve the predictive capacity of the model. The goal of our research is to quantify the information content of the observations. Following a method developed in meteorology, we employ an observation sensitivity matrix to quantify the effect of observed data on predicted data. The use of this matrix is illustrated with an example in which we adjust the permeability field of a two-phase two-dimensional reservoir model by means of a particular history matching technique, the representer method. This method particularly allows for efficient computation of the observation sensitivity matrix. Conceptually, however, the use of an observation sensitivity matrix is equally valid for other history matching techniques. In our example the information content of the updated model comes mostly (96%) from a priori knowledge and to a much lesser extent (4%) from the observations. This finding is in line with the practical experience that in computer-assisted history matching using production data the results are strongly influenced by the prior model.

Gravimetric monitoring of water influx into a gas reservoir: A numerical study based on the ensemble kalman filter

Water influx into gas fields can reduce recovery factors by 10-40%. Therefore, information about the magnitude and spatial distribution of water influx is essential for efficient management of waterdrive gas reservoirs. Modern geophysical techniques such as gravimetry may provide a direct measure of mass redistribution below the surface, yielding additional and valuable information for reservoir monitoring. In this paper, we investigate the added value of gravimetric observations for water-influx monitoring into a gas field. For this purpose, we use data assimilation with the ensemble Kalman filter (EnKF) method. To understand better the limitations of the gravimetric technique, a sensitivity study is performed. For a simplified gas-reservoir model, we assimilate the synthetic gravity measurements and estimate reservoir permeability. The updated reservoir model is used to predict the water-front position. We consider a number of possible scenarios, making various assumptions on the level of gravity measurement noise and on the distance from the gravity observation network to the reservoir formation. The results show that with increasing gravimetric noise and/or distance, the updated model permeability becomes smoother and its variance higher. Finally, we investigate the effect of a combined assimilation of gravity and production data. In the case when only production observations are used, the permeability estimates far from the wells can be erroneous, despite a very accurate history match of the data. In the case when both production and gravity data are combined within a single data assimilation framework, we obtain a considerably improved estimation of the reservoir permeability and an improved understanding of the subsurface mass flow. These results illustrate the complementarity of both types of measurements, and more generally, the experiments show clearly the added value of gravity data for monitoring water influx into a gas field. Copyright

Non-parametric Bayesian networks for parameter estimation in reservoir simulation: a graphical take on the ensemble Kalman filter (part I)

Reservoir simulation models are used both in the development of new fields and in developed fields where production forecasts are needed for investment decisions. When simulating a reservoir, one must account for the physical and chemical processes taking place in the subsurface. Rock and fluid properties are crucial when describing the flow in porous media. In this paper, the authors are concerned with estimating the permeability field of a reservoir. The problem of estimating model parameters such as permeability is often referred to as a history-matching problem in reservoir engineering. Currently, one of the most widely used methodologies which address the history-matching problem is the ensemble Kalman filter (EnKF). EnKF is a Monte Carlo implementation of the Bayesian update problem. Nevertheless, the EnKF methodology has certain limitations that encourage the search for an alternative method.For this reason, a new approach based on graphical models is proposed and studied. In particular, the graphical model chosen for this purpose is a dynamic non-parametric Bayesian network (NPBN). This is the first attempt to approach a history-matching problem in reservoir simulation using a NPBN-based method. A two-phase, two-dimensional flow model was implemented for a synthetic reservoir simulation exercise, and initial results are shown. The methods’ performances are evaluated and compared. This paper features a completely novel approach to history matching and constitutes only the first part (part I) of a more detailed investigation. For these reasons (novelty and incompleteness), many questions are left open and a number of recommendations are formulated, to be investigated in part II of the same paper.

A Case Study of the History Matching Of A Sector Of The Norne 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 Norne 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 Norne 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.

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.

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.