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Foam greatly reduces the mobility of gas in porous media, both by increasing the effective viscosity of the gas phase and by trapping a substantial fraction of the gas in place. Mechanistic models for foam mobility split the effect of foam into an effective viscosity and an effective relative permeability, which includes the effect of gas trapping. The effective gas relative permeability is represented as a function of the volume fraction of gas that flows, which depends on the pressure gradient. We test various models for effective gas relative permeability using realistic network models of a sphere pack and a sandstone. We represent the gas phase as a Bingham plastic, a Herschel-Bulkley fluid, or using two other simple models. We show the relation between the pressure gradient, gas flowing fraction, and gas mobility for these cases. Results for all the models differ strikingly from those based on the conventional percolation theory and bundle-of-tubes models as well as those used in current mechanistic foam simulators. No simple scaling law fits the relation between the flowing fraction and pressure gradient for both the sandstone and the sphere pack. A new model for gas superficial velocity as a function of pressure gradient fits our results for one fluid model in one pore network reasonably well.

In mechanistic modeling of foam in porous media, reduced gas mobility is attributed to viscous resistance of flowing foam lamellas to gas flow, while gas trapping significantly modifies relative permeability. By using pore-network models representative of real porous media, we previously developed a relationship between flowing gas fraction and pressure gradient for strong foam (high lamella density). In this study, we expand our model to describe the effects of foam strength and pore-scale apparent gas viscosity models on both relative gas permeability and effective gas viscosity. Dimensional analysis in scaling of these two rheological quantities with pressure gradient and lamella density is discussed. One of our important findings is that relative gas permeability is poorly sensitive to total lamella density while it is a strong non-linear function of flowing gas fraction, opposing to most of the existing theoretical models describing the effect of gas trapping on relative gas permeability. This is consistently observed for all the pore-scale apparent gas viscosity models. It is also found that effective gas viscosity increases exponentially with flowing lamella density. This result implies that the use of the commonly used apparent gas viscosity model for straight capillary tubes is not accurate for foam flow in porous media. In addition, shear thinning foam flow is more obvious at high flowing lamella density while Newtonian flow becomes significant at relatively low flowing lamella density. Furthermore, scaling of effective gas viscosity with flowing lamella density depends on how the later quantity is defined. Both empirical and mechanistic pore-scale apparent gas viscosity models give almost the same functional relationship between flowing gas fraction and pressure gradient. This would facilitate scaling of flow rate with pressure gradient and testing a range of shear-thinning and yield-stress behavior in a simple format. Our results necessitate the need for further improving the existing mechanistic foam modeling methods with focus on process upscaling.

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Purpose. To investigate effects of biologicals on disease-induced damage to white cabbage plants during the growing period and on yield. Methods. Informational/analytical (collection and review of publications), field research (planning and conducting experiments, records of plant damage, harvesting and accounting of yields), phytopathological (isolation and identification of pathogens), mathematical/statistical (processing of data). The following biologicals were used in he experiments: Azotobacterin liq. (Azotobacter chroococcum IMV B-7171), Ecophosphorin liq. (Bacillus megaterium IMV B-7168, Azotobacter chroococcum IMV B7171, Agrobacterium radiobacter IMV B-7246), Planrhiz liq. (Pseudomonas fluorescens), Haupsin liq. (Pseudomonas auerofaciens), Serenade ASO SC, Serenade MAX WP (Bacillus subtilis QST 713), and Trichodermin liq. (Trichoderma lignorum TD 93). Biologicals were sprayed on plants 3-4 times during the cabbage growing period. Antifungal potentials of mixtures of biologicals with fungicides were also investigated on white cabbage. Results. During the study years, Alternaria leaf spot, Fusarium wilt, black and soft rots were dominating diseases on plantations with different varieties of white cabbage. Biologicals effectively restrained the development of both fungal and bacterial diseases of white cabbage. The protective effect of the biologicals against fungal diseases averaged 45-62%, against bacterial diseases – 65-79%. The effectiveness of mixtures of biologicals and chemicals, in which fungicides were applied at minimally permissible doses, was similar to that of fungicides applied at full doses. Biologicals, due to their protective and growthstimulating properties, significantly increased the crop yield. Conclusions. The potentials of biologicals to control fungal and bacterial diseases of white cabbage during the growing period were evaluated. The biologicals effectively limited infection-inflicted damage to cabbage. The protective effect of the biologicas against various diseases of white cabbage during the growing period of different varieties averaged 45-79%. The biologicals increased the yields of late-ripening white cabbage varieties on average by 14.5–92%.