Spontaneous radial capillary impregnation across a bank of aligned micro-cylinders – Part I: Theory and model development

Neacsu, Valentin; Obaid, Ahmad Abu; Advani, Suresh G.

doi:10.1016/j.ijmultiphaseflow.2006.02.006

Cited by 25 publications

(8 citation statements)

References 29 publications

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“…A similar equation, although for co-current imbibition radially into a bundle of fibres, was obtained by Neacsu et al (2006). From geometry, the fraction of the total imbibition when the front is at R f is…”

Section: Radial Imbibitionmentioning

confidence: 75%

Spontaneous Counter-Current Imbibition into Core Samples with All Faces Open

et al. 2008

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Counter-current imbibition occurs when brine spontaneously displaces oil from a very strongly water-wet rock. Experiments are usually carried out on cylindrical core plugs which have all of their faces open, mainly because this is easiest to do and also because it appears to give the most reproducible results. The flow patterns are complex, but a reasonable approximation can be obtained by assuming piston-like advance of fronts from the radial outer face and both flat ends. This separates the flow pattern into two types: linear imbibition into cones and radial imbibition into the surrounding toroid ring. Production versus time curves have been calculated for cylinders of varying aspect ratios and other core shapes. The analytical results confirm the experimental observation that sample shape does not have much effect on the shape of the production versus time curves. Bearing in mind the inherent variability of experimental results for individual core samples, the differences would be difficult to detect in experiments. The time for imbibition to be completed scales as the characteristic length. The function given by Ma et al. (J Pet Sci Eng 18:165-178, 1997) requires only a small correction factor for agreement with the analytical result. The present analysis makes straightforward the comparison of results from the complex flow condition 123 200 G. Mason et al. of all-faces-open imbibition with results from linear and radial experiments. A comparison is made with published results. Nomenclature a L toroid − L cone (m) A Area (m 2 ) A f Area of the displacement front (m 2 ) A i Area open to imbibition in the ith direction (m 2 ) A R Area of the cylinder at a general radius, R(m 2 ) b L cone /R max C spread Factor determined by the breadth and shape of the pore size distribution d Core diameter (m) f Fraction of the core filled K Permeability (m 2 ) k rnw Relative permeability of the non-wetting phase k rw Relative permeability of the wetting phase L c Characteristic length (m) L cone Length of a cone (m) L core Core length (m) L c,Ma Characteristic length calculated from Ma's equation (m) L f Distance from the open face to the front for the cone (m) L max Length of the core for linear imbibition (m) L toroid Length of the toroid (m) M Mobility factor (Pa −1 s −1 )n Total number of surfaces open to imbibition P c Capillary pressure (Pa) P cf Capillary pressure at the imbibition front (Pa) P co Capillary pressure at the open face (Pa) P nw Pressure in the non-wetting phase (Pa) P w Pressure in the wetting phase (Pa) q nw Flow of non-wetting phase (m 3 /s) q w Flow of wetting phase (m 3 /s) q R w Flow passing through the surface of the cylinder, radius R (m 3 /s) R f Radial distance of the front from the axis (m) R end Radius of the final position of the front for the shorter toroid (m) R core Core radius (m) R sphere Radius of spherical core (m) S wf Wetting phase saturation behind the front S wi Initial wetting phase saturation t Time (s) t D Dimensionless time t end Time when imbibition ceases (s) t f Time when ...

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Section: Radial Imbibitionmentioning

confidence: 75%

Spontaneous Counter-Current Imbibition into Core Samples with All Faces Open

et al. 2008

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“…On the other hand, for the transverse tow (weft), it is accepted that the fluid front moves inward perpendicular to the fibers and it is used the mean capillary pressure given in [38] considering an hexagonal array of fibers:…”

Section: Governing Equations Boundary and Matching Conditionsmentioning

confidence: 99%

Stokes–Brinkman formulation for prediction of void formation in dual-scale fibrous reinforcements: a BEM/DR-BEM simulation

et al. 2017

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A numerical study of voids formation in dualscale fibrous reinforcements is presented. Flow fields in channels (Stokes) and tows (Brinkman) capillary ratio, jump stress coefficient and two formulations (Stokes-Brinkman and Stokes-Darcy) on the filling process, void formation and void characterization. Filling times, fluid front shapes, void size and shape, time and space evolution of the saturation, are influenced by these parameters, but voids location is not.

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“…Capillary pressure models are divided mainly into two categories-capillary rise models (Bayramli and Powell 1990;Lago and Araujo 2001;Neacsu et al 2006) and capillary pressure curve models (Leverett 1941;Grosser et al 1988;Attou and Ferschneider 2000). Those of the latter type are of interest here and hence the term capillary pressure model will be used to refer to those kinds of models.…”

Section: Capillary Pressure Modelsmentioning

confidence: 99%

An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles

Lappalainen¹,

Manninen

Alopaeus³

et al. 2008

Transp Porous Med

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Capillary pressure is considered in packed-beds of spherical particles. In the case of gas-liquid flows in packed-bed reactors, capillary pressure gradients can have a significant influence on liquid distribution and, consequently, on the overall reactor performance. In particular, capillary pressure is important for non-uniform liquid distribution, causing liquid spreading as it flows down the packing. An analytical model for capillary pressure-saturation relation is developed for the pendular and funicular regions and the factors affecting capillary pressure in the capillary region are discussed. The present model is compared to the capillary pressure models of Grosser et al. (AIChE J., 34:1850(AIChE J., 34: -1860(AIChE J., 34: , 1988 and Attou and Ferschneider (Chem. Eng. Sci., 55:491-511, 2000) and to the experiments of Dodds and Srivastava (Part Part Syst. Charact., 23:29-39, 2006) and Dullien et al. (J. Colloid Interface Sci., 127:362-372, 1989). The non-homogeneity of real packings is considered through particle size and porosity distributions. The model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity. This makes the model more suitable for porous or rough particles than for non-porous smooth particles. The main improvements of the present model are found in the pendular region, where the liquid dispersion due to capillary pressure gradients is most significant. The model can be used to improve the hydrodynamic models (e.g., CFD and cellular automata models) for packed-bed reactors, such as trickle-bed reactors, where gas, liquid, and solid phases are present. Models for such reactors have become quite common lately (Sáez and Carbonell, AIChE J., 31:52-62, 1985; K. Lappalainen (B) · V. Alopaeus Chemical Engineering and Plant Design, Nomenclatures A c Cross-sectional area (m 2 ) d Half spacing between neighboring microcylinders (m) d p Particle diameter (m) d min As defined in Eq. 5 (m) D H Hydraulic diameter (m) f Wetting efficiency J (S L ) Leverett's J -function k Permeability (m 2 ) N c Number of particle contact points per particle p c Capillary pressure (Pa) p i Pressure of phase i (Pa) r 1,2 Scaled radii of curvature R 1,2 Radii of curvature (m) R Particle radius (m) R * Mean curvature of the meniscus (m) s Perimeter (m) S L Liquid saturation V f Volume of fluid in a pendular ring (m 3 )Greek letters ε Void fraction of the packed-bed ϕ Filling angle (see Fig. 3) (rad) (x) Gamma function θ Liquid-solid contact angle (rad) θ i Holdup of phase i ρ i Density of phase i (kg · m −3 ) σ Surface tension between the wetting and the non-wetting phases (N · m −1 ) X(1 − cos ϕ)

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Spontaneous radial capillary impregnation across a bank of aligned micro-cylinders – Part I: Theory and model development

Cited by 25 publications

References 29 publications

Spontaneous Counter-Current Imbibition into Core Samples with All Faces Open

Spontaneous Counter-Current Imbibition into Core Samples with All Faces Open

Stokes–Brinkman formulation for prediction of void formation in dual-scale fibrous reinforcements: a BEM/DR-BEM simulation

An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles

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