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Hybrid integral transforms for flow development in ducts partially filled with porous media.

ABSTRACT: A hybrid numerical-analytical solution is developed for laminar flow development in a parallel plate duct partially filled with porous media. The integral transform method is employed in combination with a single domain reformulation strategy for representing the heterogeneous media within the channel. A novel eigenfunction expansion basis is proposed, including abrupt spatial variations of physical properties due to the domain transitions. The introduction of the new basis allows for a solution with similar convergence rates as in previous applications with simpler formulations, as demonstrated through a careful convergence analysis of the expansions. The inherent automatic error control characteristic of the integral transforms approach then provides benchmark results for the developing velocity profile. Moreover, a physical analysis further verifies the consistency of both the proposed expansion and the mixed symbolic-numerical code developed. A detailed verification with a finite-element commercial code is also performed.

SUBMITTER: Lisboa KM

PROVIDER: S-EPMC5806023 | biostudies-literature | 2018 Jan

REPOSITORIES: biostudies-literature

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Hybrid integral transforms for flow development in ducts partially filled with porous media.

Lisboa Kleber Marques KM Cotta Renato Machado RM

Proceedings. Mathematical, physical, and engineering sciences 20180110 2209

A hybrid numerical-analytical solution is developed for laminar flow development in a parallel plate duct partially filled with porous media. The integral transform method is employed in combination with a single domain reformulation strategy for representing the heterogeneous media within the channel. A novel eigenfunction expansion basis is proposed, including abrupt spatial variations of physical properties due to the domain transitions. The introduction of the new basis allows for a solution ...[more]

PMID: 29434513

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Project description:Laboratory measurements of capillary pressure (Pc) and the electrical resistivity index (RI) of reservoir rocks are used to calibrate well logging tools and to determine reservoir fluid distribution. Significant studies on the methods and factors affecting these measurements in rocks containing oil, gas, and water are adequately reported in the literature. However, with the advent of chemical enhanced oil recovery (EOR) methods, surfactants are mixed with injection fluids to generate foam to enhance the gas injection process. Foam is a complex and non-Newtonian fluid whose behavior in porous media is different from conventional reservoir fluids. As a result, the effect of foam on Pc and the reliability of using known rock models such as the Archie equation to fit experimental resistivity data in rocks containing foam are yet to be ascertained. In this study, we investigated the effect of foam on the behavior of both Pc and RI curves in sandstone and carbonate rocks using both porous plate and two-pole resistivity methods at ambient temperature. Our results consistently showed that for a given water saturation (Sw), the RI of a rock increases in the presence of foam than without foam. We found that, below a critical Sw, the resistivity of a rock containing foam continues to rise rapidly. We argue, based on knowledge of foam behavior in porous media, that this critical Sw represents the regime where the foam texture begins to become finer, and it is dependent on the properties of the rock and the foam. Nonetheless, the Archie model fits the experimental data of the rocks but with resulting saturation exponents that are higher than conventional gas-water rock systems. The degree of variation in the saturation exponents between the two fluid systems also depends on the rock and fluid properties. A theory is presented to explain this phenomenon. We also found that foam affects the saturation exponent in a similar way as oil-wet rocks in the sense that they decrease the cross-sectional area of water available in the pores for current flow. Foam appears to have competing and opposite effects caused by the presence of clay, micropores, and conducting minerals, which tend to lower the saturation exponent at low Sw. Finally, the Pc curve is consistently lower in foam than without foam for the same Sw.

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Hybrid integral transforms for flow development in ducts partially filled with porous media.

Publications

Hybrid integral transforms for flow development in ducts partially filled with porous media.

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