Micromodel

Foam generated in porous media consists of a gas (or a liquid) dispersed in a second interconnected wetting liquid phase, usually an aqueous surfactant solution (1). Figure 1 shows a micrograph of foam flowing in a two-dimensional etched-glass porous medium micromodel (replicated from a Kuparuk sandstone, Prudhoe Bay, Alaska (2)). Observe that the dispersion microstructure is not that of bulk foam. Rather discontinuous... 

For the wet case, the foam enters and achieves steady state after several pore volumes. A mobility reduction compared to water of about 90% ensues. However, for the dry case, there is about a one pore-volume time lag before the pressure responds. During this time, visual observations into the micromodel indicate a catas-tropic collapse of the foam at the inlet face. The liquid surfactant solution released upon collapse imbibes into the smaller pores of the medium. Once the water saturation rises to slightly above connate (ca 30%), foam enters and eventually achieves the same mobility as that injected into the wet medium. 

Figure 1. Micrograph of foam in a 1.1 pm, two dimensional etched-glass micromodel of a Kuparuk sandstone. Bright areas reflect the solid matrix while grey areas correspond to wetting aqueous surfactant solution next to the pore walls. Pore throats are about 30 to 70 /xm in size. Gas bubbles separated by lamellae (dark lines) are seen as the nonwetting "foam" phase.

Figure 2. Transient pressure drop across the porous-medium micromodel of Figure 1 for foam pregenerated in an identical upstream medium. The foam frontal advance rate is 186 m/d. In the wet case, foam advanced into the downstream micromodel which was completely saturated with aqueous surfactant solution. In the dry case, the downstream micromodel contained only air.

In order to understand the nature and mechanisms of foam flow in the reservoir, some investigators have examined the generation of foam in glass bead packs (12). Porous micromodels have also been used to represent actual porous rock in which the flow behavior of bubble-films or lamellae have been observed (13,14). Furthermore, since foaming agents often exhibit pseudo-plastic behavior in a flow situation, the flow of non-Newtonian fluid in porous media has been examined from a mathematical standpoint. However, representation of such flow in mathematical models has been reported to be still inadequate (15). Theoretical approaches, with the goal of computing the mobility of foam in a porous medium modelled by a bead or sand pack, have been attempted as well (16,17). 

For the purpose of illustration, in this paper we use a viscosity-capillarity model (Truskinovsky, 1982 Slemrod, 1983) as an artificial "micromodel",and investigate how the information about the behavior of solutions at the microscale can be used to narrow the nonuniqueness at the macroscale. The viscosity-capillarity model contains a parameter -Je with a scale of length, and the nonlinear wave equation is viewed as a limit of this "micromodel" obtained when this parameter tends to zero. As we show, the localized perturbations of the form x /-4I) can influence the choice of attractor for this type of perturbation, support (but not amplitude) vanishes as the small parameter goes to zero. Another manifestation of this effect is the essential dependence of the limiting solution on the... 

Since in this problem not only the limit but also the character of convergence matters we conclude that consistent homogenization of the micromodel should lead to a description in a broader functional space than is currently accepted. One interesting observation is that the concave part of the energy is relevant only in the region with zero measure where the singular, measure valued contribution to the solution is nontrivial (different from point mass). We remark that the situation is similar in fracture mechanics where a problem of closure at the continuum level can be addressed through the analysis of a discrete lattice (e.g. Truskinovsky, 1996). 

Glass micromodels, in high P cell (Tohidi et al., 2002) Hydrate, gas, water phase distribution Yes P, T hydrate phase vs. time (min) Typically up to 5000 psi >50 pm channels Visual location of hydrate phase during growth... 

FIGURE 6.10 Schematic of the glass micromodel apparatus (a) and the micromodel pore network (b). (Reproduced from Tohidi, B., Anderson, R., Clennell, B., Yang, J., Bashir, A., Burgass, R.W., in Proc. Fourth International Conference on Gas Hydrates, Yokohama, Japan, May 19-23, p. 761 (2002). With permission.)... 

The so-called micromodels are models of a particular component, or of a part of a cell component, conducted at molecular or atomistic level. Due to the high level of detail related to the material properties and characteristics, the information provided by such models is usually limited to the specific phenomenon analyzed, and provides only limited indications on the resulting fuel cell performance and operating conditions. However, the results of such models play a fundamental role in understanding, analyzing and designing improved solutions for SOFC. Moreover, the results of such analyses may be used as an input for macro-models, i.e. models conducted at fuel cell level. 

Several micromodels can be found in the literature on SOFC components or materials (e g. [8-15]), and the results should be taken into account when defining a mathematical model of a single cell, or stack. However, the analysis and description of such models is beyond the scope of the present book. 

Micro-scale experiments involve the microscopic observation of flowing foams in etched-glass micromodels. Here the pore dimensions are typically on the order of hundreds of micrometers. Such experiments provide valuable and rapidly obtainable qualitative information about foam behaviour in constrained media under a variety of experimental conditions, including the presence of a residual oil saturation... 

Keller AA, Blunt MJ, Roberts PV (1997) Micromodel observation of the role of oil layers in three-phase flow. Transp. Porous Media 26 277-297... 

The studies of Marsden et al. [162], Holm [164] and more recently of Trienen et al. [165], Ettinger and Radke [166,167], including the direct observations in a transparent etched-glass micromodels [158,168,169], have established that the bubble size is almost equal to the... 

Gas mobility in the presence of a foam is dominated by foam texture (bubble size) [171]. The strong fall in permeability in the presence of a foam is a result of foam trapping established not only in the macroscopic studies but by the direct observations of transparent micromodels [153,158] as well. Foam trapping is a batch process the immobile foam can become mobile with time and vice versa [158]. 

Mast, in a pioneering 1972 paper, reported visual observations of foam flow in etched glass micromodels (37 ) His observations showed that some of the conflicting claims about the properties of foam flow in porous media were probably due simply to the dominance of different mechanisms under the various conditions employed by the separate researchers (37). Mast observed most of the various mechanisms of dispersion formation, flow, and breakdown that are now believed to control the sweep control properties of surfactant-based mobility control (37,39-41). 

A high-pressure micromodel system has been constructed to visually investigate foam formation and flow behavior. This system uses glass plates, or micromodels, with the pattern of a pore network etched into them, to serve as a transparent porous medium. These micromodels can be suspended in a confining fluid in a pressure vessel, allowing them to be operated at high pressure and temperature. Because of this pressure capability, reservoir fluids can be used in the micromodel, and any effects of phase behavior or pressure- and temperature-dependent properties on foam flow can be examined. 

The high-pressure and temperature micromodel system has been used in this study to investigate the formation, flow behavior and stability of foams. Micromodel etching patterns were made from binary images of rock thin sections and from other designs for a comparison of pore effects. These experiments show how simultaneous injection of gas and surfactant solution can give better sweep efficiency on a micro-scale in comparison to slug injection. 

The micromodel is located in the mid-section of the pressure vessel. It is seated in a slot where the feed ports exit the mid-section and is clamped down by restraining bars. The holes tapped in the micromodel are aligned with the feed port exits, and a seal is maintained by 0-rings seated around these exits. This design differs from the Campbell-Orr pressure vessel which uses tubing fitted to C-clamps to carry fluids to and from the micromodel. The design employed here restricts the size of the micromodels to a particular set of specifications, but does provide a more secure way of pressurizing the micromodel. 

Micromodel floods were recorded on videotape for later analysis. A television camera with a zoom lens allowed magnification levels from 33x to 333x as measured on the monitor s screen. A Fujinon 35mm lens was used for larger fields of view. Recording was made in time lapse for replay in real time, allowing up to 10 days worth of recording on a two-hour tape. 

Figure 1. Micromodel Pressure Vessel Exploded View...

The etching of the micromodels used in this study was performed by M. Graham of Adobe Labs Co. using a technique developed by B.T. Campbell and I. Chatzis. ... 

Table II lists the micromodel experiments performed in this study. Only two micromodels, the Reservoir Sandstone (RS) and the "Patio Stone (PS), were used. In these experiments the performance of different injection schemes and the effects of surfactant on gas displacement of water were investigated.

To quantify micromodel flow characteristics, the mobility-thickness, M-t, and the permeability-thickness, k-t, can be calculated. These quantities are used here instead of mobility and permeability because the flow is only two-dimensional. Mobility-thickness is defined as... 

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