An exact analytical model for fluid flow through finite rock matrix block with special saturation function

This paper, together with a companion paper which follows, describes a many-faceted experimental investigation aimed at determining basic characteristics of fluid flow through deformable porous media. A major focus of the work is to establish the validity and the range of applicability of a simple analytical model for the fluid flow. The present paper describes experiments with a gas (air) as the working fluid, while the companion paper (Part II) deals with liquid-flow (i.e., water-flow) experiments. The experiments encompassed three distinct phases. In the first phase, the stress-deformation characteristics were measured (without fluid flow). In the second, flow-related material properties that are relevant to the analytical model (e.g., permeability, Forchheimer coefficient) were determined. The third phase consisted of measurements of mass flow rate as a function of applied pressure differential. The results of the first two phases were used as input to the analytical model, which yielded predictions of mass flow versus applied pressure. These predictions were shown to be in very good agreement with the experimental results, for those conditions where the model is applicable. Two unusual features of the participating deformable materials (polyurethane foams) were encountered, namely, a decrease of cross-sectional area with increasing compression and a slow relaxation of the internal stresses at a fixed compression.

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THREE-DIMENSIONAL SIMULATION OF FLUID FLOW THROUGH A DISCRETE FRACTURE AND MATRIX

10.32008/geolinks2021/b1/v3/33 ◽

2021 ◽

Author(s):

Kunwar Mrityunjai Sharma ◽

Tariq Anwar Ansari

Keyword(s):

Fluid Flow ◽

Oil And Gas ◽

Flow Behavior ◽

Gas Production ◽

Geothermal System ◽

Porous Rocks ◽

Permeability Model ◽

Matrix Block ◽

The Matrix ◽

Flow Through

The study of fluid flow mechanics in fractured porous rocks is crucial in the area of oil and gas production industries, enhanced geothermal system (EGS), CO2 sequestration, disposal of nuclear waste in deep geological repositories (DGR), etc. There are usually two types of flows in fractured rockmass setting. The dominant flow occurs through the fractures whereas there is also a slow movement of fluid through the matrix block. The fluid movement between fracture and matrix is often continuous across the fracture. The present study focuses on the development of a numerical model which can simulate the flow behavior through fracture and matrix simultaneously, which is also known as dual permeability model. To simulate this problem, a 3D model is built in COMSOL Multiphysics 4.3a where a cylindrical geometry is made, and a fracture is defined parallel to the axis of the geometry. The asperity of the fracture is defined by a variable ‘a’ which varies along the x-axis, in such a way that increases the value of ‘a’ alters the geometry of fracture and increases the roughness of fracture. Darcy flow physics is used to simulate the situation with known parameters like porosity, permeability, storage coefficient, etc. Pressure is applied as a boundary condition at two ends of the geometry which acts as driving force for fluid to flow through the block. The influence of fracture asperity on the flow behavior is examined by doing the parametric study and the study shows the decrement in the velocity magnitude with an increase in asperity. The formation of dual flow velocity regime, one along the defined fracture and the other along with the matrix, indicates the efficiency of the developed dual-porosity and permeability model.

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Characterization of Capillary Flow Within a Homogenously Dispersed Array of Vertical Micropillars

ASME 2010 8th International Conference on Nanochannels, Microchannels, and Minichannels: Parts A and B ◽

10.1115/fedsm-icnmm2010-30526 ◽

2010 ◽

Cited By ~ 1

Author(s):

Conan Zhang ◽

Carlos H. Hidrovo

Keyword(s):

Fluid Flow ◽

Analytical Solution ◽

Analytical Model ◽

Capillary Flow ◽

Capillary Forces ◽

Auxiliary Equipment ◽

Geometric Conditions ◽

Wick Structure ◽

Vertically Aligned ◽

Flow Through

When considering fluidic devices at the micron length scale, surface tension forces become dominant relative to body forces. Albeit smaller than mechanical and electrical pumps, capillary forces are commonly exploited as a mechanism to drive fluid flow. Unlike pumps, capillary driven flows are passive in nature and are not dependent on auxiliary equipment to drive fluid flow. Although beneficial from an energy standpoint, the lack of a supplementary driving potential causes the flow to be limited by the wick structure dimensions that generate the capillary forces. Subsequently, investigation into the contributions of the wick structure must be performed in order to optimize the fluid flow through a capillary structure. General capillary theory states that capillary forces increase inversely proportional to the pore radius. Consequently, arrays of vertically aligned nanopillars grown on silicon substrates are considered for fluid flow optimization due to their small pores. To simulate these nanopillars, an ab initio analysis was done on a homogenously dispersed array of vertically aligned pillars. An analytical solution to predict the maximum achievable capillary flow with respect to the structure dimensions was found through this method. Subsequently, this analytical solution can be used to produce a set of optimal geometric conditions that would induce the maximum capillary flow through a wick comprised of vertically aligned pillars. Experimental results are also presented to validate the analytical solution. Homogeneously dispersed cylindrical pillars were created on silicon wafers via reactive ion etching to reconstruct the geometry assumed by the analytical solution. The capillary limit was found for structures with varying geometric dimensions. By contrasting the empirical data with the values predicted by the analytical model, the validity of the analytical model was found to be in good agreement.

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