The purpose of this study is to investigate factors that affect the formation of fluid banks during gravity-driven counter-current flow in porous media. To our knowledge, development of a fluid bank has been observed in only one previous counter-current flow experiment, although there are some hints of fluid banks in other experiments. We have undertaken experimental and simulation studies to confirm the presence of such banks and to delineate factors which enhance or inhibit their formation. Experiments were performed using glass bead packs and X-ray Computed Tomography to monitor saturation distribution as a function of time. The simulation approach considers saturation history at every point in the sample, defining conditions at each time point from hysteresis in capillary pressure and relative permeability. The model proved to reproduce experimental observations accurately. The experiments and associated model show that a minimal vertical sample height is needed for the development of a fluid bank. In addition, round sample boundaries and higher average nonwetting phase saturation tend to prevent the formation of a bank. The validated model can improve our ability to predict and optimize counter-current flow processes, both in the laboratory and in the field (e.g. exploration and hydrocarbon extraction).

Résumé -Caractérisation des erreurs de mesure des données sismiques 4D et des données de production par l'algorithme EM -La caractérisation des erreurs de mesure est cruciale pour l'utilisation de l'approche de Bayes afin de conditionner les modèles de réservoir aux données dynamiques, c'est-à-dire les données sismiques 4D ainsi que les données de production, par l'history matching automatique. Dans la littérature, les erreurs de mesure pour chaque type de données sont généralement estimées en appliquant la technique de lissage sur tout le domaine des données engendrant, de ce fait, un surlissage des données (en particulier aux alentour des points pour lesquels les données réelles changent de façon drastique), ainsi qu'une surestimation des erreurs de mesure. Cet article présente une nouvelle procédure pour l'estimation de l'erreur de mesure. La méthode developpée ici, est basée sur l'algorithme EM (Expectation-Maximization) modifié, combiné à un fit polynomial mouvant. Cette méthode fournit une estimation de la moyenne et de la covariance des erreurs de mesure. La procédure évite le lissage sur les discontinuités. L'algorithme est appliqué aussi bien aux données sismiques 4D synthétiques qu'aux données de champs ainsi qu'aux données de production. Les résultats sont comparés à ceux obtenus avec des algorithmes de lissage plus standard à fenêtre mouvante. Concernant l'exemple de données synthétiques, la procédure basée sur l'algorithme EM produit des résultats supé-rieursà ceux obtenus par des méthodes basées sur une sorte de moyenne mouvante. En ce qui concerne les données de champs, l'EM semble aussi donner un résultat raisonnable. Abstract -Characterization of the Measurement Error in Time-Lapse Seismic Data and Production Data with an EM Algorithm -The characterization of measurement error is important if one uses a

The model parameters we estimate are the porosity and log-permeabilities of each gridblock and parameters defining relative permeability curves. Let m be a vector of the model parameters. In the Bayesian approach, m is considered to be a random vector. We assume that m has a prior multivariate Gaussian distribution with covariance matrix C M and prior mean m prior . The model parameters defining the relative permeability curves are assumed uncorrelated with the gridblock porosities/log-permeabilities. We store all the observed data, such as BHP (bottomhole pressure), WOR and GOR in the vector d obs . The corresponding predicted data for a given m are represented by d g m = ( ) .

Fluid banks sometimes form during gravity-driven counter-current flow in certain natural reservoir processes. Prediction of flow performance in such systems depends on our understanding of the bank-formation process. Traditional modeling methods using a single capillary pressure curve based on a final saturation distribution have successfully simulated counter-current flow without fluid banks. However, it has been difficult to simulate counter-current flow with fluid banks. In this paper, we describe the successful saturation-history-dependent modeling of counter-current flow experiments that result in fluid banks. The method used to simulate the experiments takes into account hysteresis in capillary pressure and relative permeabilities. Each spatial element in the model follows a distinct trajectory on the capillary pressure versus saturation map, which consists of the capillary hysteresis loop and the associated capillary pressure scanning curves. The new modeling method successfully captured the formation of the fluid banks observed in the experiments, including their development with time. Results show that bank formation is favored where the p c -versus-saturation slope is low. Experiments documented in the literature that exhibited formation of fluid banks were also successfully simulated.