Summary Flow experiments involving cocurrent and countercurrent spontaneous water/oil imbibition were performed on the same laterally coated sample of a natural porous medium with local saturation measurements and various boundary conditions. The experiments with countercurrent imbibition showed slower oil recovery, a smoother water/oil front, and slightly lower ultimate oil recovery than those with predominantly cocurrent imbibition. Numerical simulations revealed that the relative permeabilities that enabled good prediction of countercurrent oil recovery rate are about 30% less than the conventional cocurrent relative permeabilities at a given water saturation. Viscous coupling is assumed to permeabilities at a given water saturation. Viscous coupling is assumed to be the origin of this difference. A new formulation of Darcy equations that uses a matrix of mobilities was found to be in qualitative agreement with experimental results. Introduction Fractured reservoirs contain a substantial share of the world's oil reserves. Forecasts of the efficiency of a water-injection process for such reservoirs remain difficult because of poor knowledge of the different fracture networks and the individual production behavior of the matrix blocks in contact with water; i.e., each block produces its oil more or less independently from its neighbors produces its oil more or less independently from its neighbors under the combined effects of gravity and capillarity. Two-phase displacement of this kind is called spontaneous or free imbibition, and the mechanisms controlling such flow are analyzed in this study. Spontaneous imbibition involves both cocurrent and countercurrent flows in proportions that depend on the ratio of gravity to capillary forces and on the conditions applied at the boundaries of the block. The main concern has been finding a reliable procedure for scaling up laboratory imbibition tests performed on small cores. Experimental and numerical approaches have been considered. In the experimental approach, the scaling laws that apply to waterflooding were extended to spontaneous imbibition. Kyte proposed a centrifuging method for scaling up the effect of both gravity and capillary forces. Lefebvre du Prey, however, found that, when this centrifuging method was used to keep the ratio of gravity to capillary forces constant, a large discrepancy existed between the scaled-up recovery curves corresponding to different-sized blocks. The validity of standard macroscopic equations of two-phase displacements then became questionable because relative permeabilities are defined for fluids moving in the same direction and not permeabilities are defined for fluids moving in the same direction and not for countercurrent flows. Other possible origins of this discrepancy were suggested, such as imperfect knowledge of the boundary conditions and local heterogeneities of the porous medium that cannot be scaled up. Jacquin et al. therefore undertook a careful study of the mechanisms of spontaneous imbibition. Spontaneous imbibition tests (ID) on laterally coated sandstone samples 9.8 to 39 in. [25 to 100 cm] in length gave results in good agreement with conventional scaling laws. Therefore, the experimental scaling-up procedure requires numerous rules to be respected. The selection of the rock sample and the applied boundary conditions used for performing the imbibition test can strongly influence the results and prevent scaling up to reservoirblock sizes. The numerical method may be an alternative for solving this problem because the heterogeneities of the reservoir and various boundary conditions can easily be considered. It is necessary, however, to introduce the exact capillary pressure and relative permeability curves. Blair and Torsaeter and Silseth showed that these curves have an important impact on the oil recovery rate, with capillary pressures probably having a stronger effect than relative permeabilities. Some questions arise about using water/oil relative permeabilities, always determined from a cocurrent waterflood, to predict permeabilities, always determined from a cocurrent waterflood, to predict countercurrent imbibition flows. Unfortunately, there are very few experimental determinations of countercurrent relative permeabilities.
This paper describes experimental studies of spontaneous imbibition of oil by water in a low-permeability outcrop chalk. At constant and high interfacial tension (IFT), the importance of capillary forces and the existence of a predominantly countercurrent mechanism were established. Additional experiments were performed to investigate the influence of length and of various boundary conditions. In another investigation, we modified the IFT at the sample boundary by using pairs of conjugate phases of the n-hexane/ethanol/brine ternary system. Final recovery increased when IFT was lowered. We give a numerical interpretation for this last result.
Résumé -Simulation des réservoirs fracturés : un défi et un enjeu -Au cours des années récentes, la prise de conscience du rôle des fractures sur la production et la récupération des champs est devenue de plus en plus forte au sein de la communauté pétrolière. Aussi beaucoup d'efforts ont-ils été consacrés à la détection des fractures et à l'analyse de leur impact sur la production. Toutefois, la prise en considération de ces observations dans les choix de développement des champs passe par la simulation de réservoir. Cet article traite des spécificités propres aux réservoirs fracturés et qui font de leur simulation à la fois un défi et un enjeu. En effet, l'intégration des fractures dans un modèle de simulation des écoulements n'est pas immédiate en raison du difficile passage à opérer entre l'observation géologique du réseau de fractures/failles et le rôle exercé par ce réseau sur des mécanismes de récupération souvent complexes. Sachant de plus que les fractures peuvent aussi bien freiner que promouvoir la production, la simulation des réservoirs fracturés peut être considérée comme un défi technique de grand enjeu. Cet article décrit ce contexte propre aux réservoirs fracturés en tant qu'introduction à deux articles techniques dédiés à la simulation de réservoir en double milieu. Bien qu'elle constitue un autre aspect majeur de l'étude de tout réservoir fracturé, la caractérisation géologique des fractures n'est pas discutée ici, mais seulement évoquée en raison d'une intégration croissante des aspects statique et dynamique. Abstract
Quantitative systems pharmacology (QSP) modeling has become increasingly important in pharmaceutical research and development, and is a powerful tool to gain mechanistic insights into the complex dynamics of biological systems in response to drug treatment. However, even once a suitable mathematical framework to describe the pathophysiology and mechanisms of interest is established, final model calibration and the exploration of variability can be challenging and time consuming. QSP models are often formulated as multi-scale, multi-compartment nonlinear systems of ordinary differential equations. Commonly accepted modeling strategies, workflows, and tools have promise to greatly improve the efficiency of QSP methods and improve productivity. In this paper, we present the QSP Toolbox, a set of functions, structure array conventions, and class definitions that computationally implement critical elements of QSP workflows including data integration, model calibration, and variability exploration. We present the application of the toolbox to an ordinary differential equations-based model for antibody drug conjugates. As opposed to a single stepwise reference model calibration, the toolbox also facilitates simultaneous parameter optimization and variation across multiple in vitro, in vivo, and clinical assays to more comprehensively generate alternate mechanistic hypotheses that are in quantitative agreement with available data. The toolbox also includes scripts for developing and applying virtual populations to mechanistic exploration of biomarkers and efficacy. We anticipate that the QSP Toolbox will be a useful resource that will facilitate implementation, evaluation, and sharing of new methodologies in a common framework that will greatly benefit the community.
The methane and nitrogen diffusion experiments described in this paper enlighten the mechanisms of oil recovery from gas flooded fractured reservoirs. D. Morell, SPE, B. Bourbiaux, SPE, M. Latil, SPE, Institut Fran~ais du Petrole, and B. Thiebot, SPE, Total-CFP.SUMMARY The combined effects of gas diffusion and stripping in the matrix blocks of light-oil fractured reservoirs subjected to methane or nitrogen gas flooding are experimentally studied with a specific automated apparatus. ID and 3D experiments are performed with a methane pentane mixture. In addition to hydrocarbon recovery, local saturations are measured using a gamma-ray attenuation technique.Most of the pentane in place is recovered within several weeks. Two main differences appear between methane and nitrogen diffusion tests: (a) pentane recovery is about twice as fast with methane as with nitrogen, and (b) saturation profiles reveal a strong capillary end effect fornitrogen injection with an accumulation ofliquid near the fissure (lD).Compositional simulations, including diffusion and capillary phenomena, show that diffusion and Darcy flow take part in the recovery process.
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