Validation of Non-darcy Well Models Using Direct Numerical Simulation

Гаранжа, В. А.; Konshin, V. N.; Lyons, Stephen L.; Papavassiliou, Dimitrios V.; Qin, Guan

doi:10.1007/3-540-45467-5_12

Cited by 7 publications

(8 citation statements)

References 5 publications

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“…However, its inclusion dramatically increases the expense of numerical simulation with a high order of approximation (Garanzha et al, 2000). A criterion for predicting non-Darcy flow in porous media is needed.…”

Section: Introductionmentioning

confidence: 99%

A Criterion for Non-Darcy Flow in Porous Media

2006

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Non-Darcy behavior is important for describing fluid flow in porous media in situations where high velocity occurs. A criterion to identify the beginning of non-Darcy flow is needed. Two types of criteria, the Reynolds number and the Forchheimer number, have been used in the past for identifying the beginning of non-Darcy flow. Because each of these criteria has different versions of definitions, consistent results cannot be achieved. Based on a review of previous work, the Forchheimer number is revised and recommended here as a criterion for identifying non-Darcy flow in porous media. Physically, this revised Forchheimer number has the advantage of clear meaning and wide applicability. It equals the ratio of pressure drop caused by liquid-solid interactions to that by viscous resistance. It is directly related to the non-Darcy effect. Forchheimer numbers are experimentally determined for nitrogen flow in Dakota sandstone, Indiana limestone and Berea sandstone at flowrates varying four orders of magnitude. These results indicate that superficial velocity in the rocks increases non-linearly with the Forchheimer number. The critical Forchheimer number for non-Darcy flow is expressed in terms of the critical nonDarcy effect. Considering a 10% non-Darcy effect, the critical Forchheimer number would be 0.11.

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Section: Introductionmentioning

confidence: 99%

A Criterion for Non-Darcy Flow in Porous Media

2006

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“…Usually, Darcy's law depicts fluid flow behavior in porous media 34 . According to Darcy's law, the pressure gradient is linearly proportional to the fluid velocity in the porous material.…”

Section: Mathematical Procedures Of Darcian's and Forchheimer's Permementioning

confidence: 99%

Effect of Flow Configuration on Darcian and Forchheimer Permeabilities Determination in a Porous Composite Tube

Najmi

Tabach

Chetehouna³

et al. 2015

20th AIAA International Space Planes and Hypersonic Systems and Technologies Conference

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Using Fuel Cell on board of aircraft imposes to extract light species (such as Hydrogen and light hydrocarbons) from the liquid fuel which is stored and used, possibly attemperatures where a fuel pyrolysis occurs. Natural porosity of composite material could be used to filtrate the selected species. Hence the permeability of the porous media becomes one of the key parameter to be accurately measured. It is often determined experimentally in laboratory with disc samples (outlet of the flow is achieved through the porous material) and normal flow. However, this configuration is far from the realistic one consisting of tubes (a main flow is found additionally to the one through the material, tangential permeability). Therefore, the effect of a second outlet on the Darcy's and Forchheimer's permeabilities characterization should be studied (despite the permeability is an intrinsic property of the material itself and it should not be dependent on the test apparatus). This paper focuses on a new way of using an existing test bench for the determination of Darcy's and Forchheimer's permeabilities of C/SiC porous composite tube by taking two outlets into account. Operating parameters (temperature, pressure and mass flow rate) are measured for three different configurations: i) secondary outlet (S.O) is 0% open ii) S.O is 50% open and iii) S.O is 100% open. Then Darcy's and Forchheimer's permeabilities are computed by ISO and P 2 methodsusing a direct search algorithm. Obtained results from different methods are compared and discussed. They are in agreement with the literature data which guarantees the reliability of the test bench and of related measures. Nomenclature Acronym CMC = Ceramic Matrix Composite PO/SO ratio = ratio of the flowrate from the Primary Outlet over the one from the Secondary Outlet P.O = Primary outlet 1 2 S.O = Secondary outlet LatinLetters ag = Grain area dg = Grain diameter dp = Pore diameter KD = Darcian's permeability KF = Forccheimer's permeability L = Length Pinlet = Pressure inlet Poutlet = Pressure outlet Re = Reynolds pore number T = Temperature V = Velocity Greek Letters ε = Overall open porosity µ = Dynamic viscosity ρ = Density

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“…and J i is the Jacobian (7). In this form, it is seen that OE˙i , « i is the Jacobian matrix of mapping (6) T are flux-equivalent to operations on q i in T i [1,2].…”

Section: Shape Function and Specific Dischargementioning

confidence: 99%

“…The first candidate, O ! ı i , results from earlier work with quadrilateral [3,5,7] and hexahedral [8] discretizations in which the test function is taken proportional to @r=@ as defined in (6); the resulting function is…”

Section: Test Function and Pressure Gradientmentioning

confidence: 99%

Application of the control volume mixed finite element method to a triangular discretization

Naff

2011

Numerical Meth Engineering

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SUMMARYA two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011.

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Validation of Non-darcy Well Models Using Direct Numerical Simulation

Cited by 7 publications

References 5 publications

A Criterion for Non-Darcy Flow in Porous Media

A Criterion for Non-Darcy Flow in Porous Media

Effect of Flow Configuration on Darcian and Forchheimer Permeabilities Determination in a Porous Composite Tube

Application of the control volume mixed finite element method to a triangular discretization

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