Countercurrent imbibition is an important oil recovery mechanism in fractured reservoirs. The imbibition process can be described by a nonlinear diffusion equation that has self-similar solutions. In this paper, we use the diffusion equation to conduct numerical experiments of countercurrent imbibition in a single matrix block to identify flow characteristics. The result demonstrates that the widely-used Aronofsky et al. exponential relationship is only valid for cases where diffusion coefficients are constant. The nonlinear diffusion equations in one and two-dimensions are analytically solved using a relative flow rate concept to simplify the analysis. The result is a new understanding regarding the effects of various parameters such as capillary pressure, relative permeability, mobility ratio, and fractional flow on countercurrent imbibition. The solutions can be directly used to modify an existing single porosity model to a dual porosity model for simulating fractured reservoirs. Results show that our approach provides fairly good accuracy compared to a full-scale dual porosity model with little increase in computation time over single porosity modeling. Introduction The most efficient approach to the numerical simulation of naturally fractured reservoirs appears to be the dual porosity model, proposed by Barenblatt et al. and introduced to the petroleum industry by Warren and Root. Countercurrent imbibition displacement of oil by water in matrix blocks is an important recovery mechanism in fractured reservoirs, since most recoverable oil is present in low-permeability rocks. Modeling of imbibition as a diffusion process is not new to petroleum engineering (Handy, Blair, Lefebvre Du Prey), although it is only in the past few years that researchers have modeled fluid flow between a matrix block and surrounding fractures through a capillary diffusion process in a dual porosity model (Bech et al., Beckner et al., Douglas et al., Dutra and Aziz, Kazemi et al.). However, this approach is only applicable to incompressible or slightly compressible fluid systems. Aronofsky et al. assumed that the oil recovery of a single rock matrix due to imbibition declines exponentially with time. They also assumed that a fractured reservoir is composed of a number of identical rock matrix blocks and that the performance of each block can be integrated to predict total reservoir performance. Aronofsky et al's relationship has been used by several researchers for matrix/fracture transfer flow in fractured reservoir studies (de Swaan, Kazemi et al., Dutra and Aziz). Handy studied a simplified diffusion equation for a water-gas two-phase system by assuming negligible pressure gradient in the gas phase both ahead and behind the imbibing water front in a piston-like displacement. Based on theoretical and experimental investigations, Handy concluded that a linear relationship applies when plotting the square of the volume of water imbibed against time for water imbibing for a variety of rock properties. Blair presented a numerical study of countercurrent imbibition in porous rocks. P. 491

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The magnetic properties of ultrathin (1 -5 monolayer) Fe films on Ag(100) substrates were investigated using SQUID magnetometry.Films were grown in pairs (one bulklike, the other thin) and characterized in aitu by low-energy electron diffraction, Auger spectroscopy, and the surface magneto-optic Kerr effect. The films were then capped with Au and studied with a SQUID magnetometer over the temperature range 2 -340 K. We report here a direct observation of enhanced magnetic moments for Fe on Ag(100), with interface moments enhanced as much as 29%.