Approche probabiliste des milieux poreux hétérogènes ou fracturés en relation avec les écoulements diphasiques Probabilistic Approach to Heterogeneous Or Fractured Porous Media in Relation to Two-Phase Flows

La prise en compte des particularités structurales des gisements pétroliers fracturés ou hétérogènes est nécessaire à l'amélioration des prévisions de production. La description de ce type de gisements relève d'une approche probabiliste, qui conduit à une estimation des caractéristiques de la roche réservoir : distribution des dimensions des blocs d'un réservoir fissuré, échelles d'hétérogénéité. Ces caractéristiques sont introduites dans les modèles déterministes qui décrivent l'écoulement des fluides. On présente en particulier les problèmes que pose la transposition au gisement des résultats obtenus au laboratoire sur petits échantillons : changement d'échelle géométrique, estimation de la récupération finale et de l'évolution de la production en fonction du temps. <br> The structural features of fractured or heterogenous oil fields must be taken into consideration to improve production forecasting. The description of such fields is based on a probabilistic approach leading to an estimate of the characteristics of the reservoir rock, i. e. distribution of the block sizes of a fissured reservoir, scales of heterogeneity. These characteristics are fed into deterministic models that describe fluid flows. Special attention is paid to problems raised by the transposition of laboratory results obtained on small samples to a field. Such problems include the change in geometric scale, the estimating of ultimate recovery and how production will evolve in time

Capillary rise between closely spaced plates : effect of Van der Waals forces

The capillary rise of a perfectly wetting fluid, between two parallel plates (2 R apart), depends on the thickness of the wetting film. Moldover and Gammon [1] proposed a reduction of the effective spacing between plates 2 Reff (to be included in Jurin's law) such that R — Reff is exactly equal to Z(h) (the thickness of a film spread on a single plate). We show that the film is thickened due to the second plate, and that R - Reff = 1.5 Z(h). The comparison between theory and the data of Moldover and Gammon on SF6 is thereby improved. The present analysis is restricted to non-retarded Van der Waals forces.La hauteur capillaire h d'un fluide parfaitement mouillant entre deux plaques parallèles (distantes de 2 R) dépend de l'épaisseur du film à la paroi. Moldover et Gammon [1] ont proposé une réduction de la distance effective entre plaques 2 Reff (à insérer dans la loi de Jurin) telle que R — Reff soit exactement égal à Z(h) (épaisseur d'un film sur une plaque unique). Nous montrons que le film est en fait épaissi à cause de la présence de la 2e plaque, et que R - Reff = 1,5 Z(h). Ceci améliore la comparaison entre la théorie et les données de Moldover et Gammon sur SF 6. L'analyse est limitée à des forces de Van der Waals non retardées

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

The spontaneous capillary-driven filling of microchannels is important for a wide range of applications. These channels are often rectangular in cross-section, can be closed or open, and horizontal or vertically orientated. In this work, we develop the theory for capillary imbibition and rise in channels of rectangular cross-section, taking into account rigidified and non-rigidified boundary conditions for the liquid–air interfaces and the effects of surface topography assuming Wenzel or Cassie-Baxter states. We provide simple interpolation formulae for the viscous friction associated with flow through rectangular cross-section channels as a function of aspect ratio. We derive a dimensionless cross-over time, Tc, below which the exact numerical solution can be approximated by the Bousanquet solution and above which by the visco-gravitational solution. For capillary rise heights significantly below the equilibrium height, this cross-over time is Tc ≈ (3Xe/2)^(2/3) and has an associated dimensionless cross-over rise height Xc ≈ (3Xe/2)^(1/3), where Xe = 1/G is the dimensionless equilibrium rise height and G is a dimensionless form of the acceleration due to gravity. We also show from wetting considerations that for rectangular channels, fingers of a wetting liquid can be expected to imbibe in advance of the main meniscus along the corners of the channel walls. We test the theory via capillary rise experiments using polydimethylsiloxane oils of viscosity 96.0, 48.0, 19.2 and 4.8 mPa s within a range of closed square tubes and open rectangular cross-section channels with SU-8 walls. We show that the capillary rise heights can be fitted using the exact numerical solution and that these are similar to fits using the analytical visco-gravitational solution. The viscous friction contribution was found to be slightly higher than predicted by theory assuming a non-rigidified liquid–air boundary, but far below that for a rigidified boundary, which was recently reported for imbibition into horizontally mounted open microchannels. In these experiments we also observed fingers of liquid spreading along the internal edges of the channels in advance of the main body of liquid consistent with wetting expectations. We briefly discuss the implications of these observations for the design of microfluidic systems