The Effect of Inlet and Exit Pressure-Drop on the Determination of Porous Media Permeability and Form Coefficient

2005 ◽  
Author(s):  
Christian Naaktgeboren ◽  
Paul S. Krueger ◽  
Jose´ L. Lage
Keyword(s):  
Reynolds Number ◽  
Porous Medium ◽  
Porous Media ◽  
Pressure Drop ◽  
Turbulent Pipe Flow ◽  
Flow Adjustment ◽  
Medium Length ◽  
Exit Pressure ◽  
Flow Through

The determination of permeability and form coefficient, defined by the Hazen-Dupuit-Darcy (HDD) equation of flow through a porous medium, requires the measurement of the pressure-drop per unit length caused by the medium. The pressure-drop emerging from flow adjustment effects between the porous medium and the surrounding clear fluid, however, is not related to the porous medium length. Hence, for situations in which the entrance and exit pressure-drops are not negligible, as one would expect for short porous media, the determination of the hydraulic parameters using the HDD equation is hindered. A criterion for determining the relative importance of entrance and exit pressure-drop effects, as compared to core effect, is then of practical and fundamental interest. This aspect is investigated analytically and numerically considering flow through a thin planar restriction placed in a circular pipe. Once the pressure-drop across the restriction is found, the results are then compared to the pressure-drop imposed by an obstructive section having the same dimension as the restriction but finite length, playing the role of the least restrictive porous medium core. This comparison yields a conservative estimate of the porous medium length necessary for neglecting entrance and exit pressure-drop effects. Results show that inlet and exit pressure-drop effects become increasingly important compared to core effects as the porosity decreases and Reynolds number increases for both laminar and turbulent flow regimes. (Correlations based on experimental results available in the literature are employed for turbulent pipe flow). The analysis also shows why the HDD equation breaks down when considering flow through porous media where the entrance and exit pressure-drop effects are not negligible, and how modified permeability and form coefficients become necessary to characterize this type of porous media. Curve-fits accurate to within 2.5% were obtained for the modified permeability and form coefficients of the planar restriction with Reynolds number ranging from 0.01 to 100 and porosity from 0.0625 to 0.909.

Inlet and Outlet Pressure-Drop Effects on the Determination of Permeability and Form Coefficient of a Porous Medium

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
C. Naaktgeboren ◽  
P. S. Krueger ◽  
J. L. Lage
Keyword(s):  
Porous Medium ◽  
Pressure Drop ◽  
Parallel Plates ◽  
Pressure Drops ◽  
Outlet Pressure ◽  
Medium Length ◽  
Laminar And Turbulent Flow ◽  
Flow Through ◽  
Definition Of

The determination of permeability K and form coefficient C, defined by the Hazen-Dupuit-Darcy (HDD) equation of flow through a porous medium, requires the measurement of the total pressure drop caused by the porous medium (i.e., inlet, core, and outlet) per unit of porous medium length. The inlet and outlet pressure-drop contributions, however, are not related to the porous medium length. Hence, for situations in which these pressure drops are not negligible, e.g., for short or very permeable porous media core, the definition of K and C via the HDD equation becomes ambiguous. This aspect is investigated analytically and numerically using the flow through a restriction in circular pipe and parallel plates channels. Results show that inlet and outlet pressure-drop effects become increasingly important when the inlet and outlet fluid surface-fraction φ decreases and the Reynolds number Re increases for both laminar and turbulent flow regimes. A conservative estimate of the minimum porous medium length beyond which the core pressure drop predominates over the inlet and outlet pressure drop is obtained by considering a least restrictive porous medium core. Finally, modified K and C are proposed and predictive equations, accurate to within 2.5%, are obtained for both channel configurations with Re ranging from 10−2 to 102 and φ from 6% to 95%.

scholarly journals New Approach for Determining Tortuosity in Fibrous Porous Media

2010 ◽  
Vol 5 (3) ◽  
pp. 155892501000500 ◽  
Author(s):  
Rahul Vallabh ◽  
Pamela Banks-Lee ◽  
Abdel-Fattah Seyam
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fiber Diameter ◽  
Empirical Relationship ◽  
Air Permeability ◽  
New Approach ◽  
Upper Limits ◽  
Fibrous Porous Media ◽  
Flow Through

A method to determine tortuosity in a fibrous porous medium is proposed. A new approach for sample preparation and testing has been followed to establish a relationship between air permeability and fiberweb thickness which formed the basis for the determination of tortuosity in fibrous porous media. An empirical relationship between tortuosity and fiberweb structural properties including porosity, fiber diameter and fiberweb thickness has been proposed unlike the models in the literature which have expressed tortuosity as a function of porosity only. Transverse air flow through a fibrous porous media increasingly becomes less tortuous with increasing porosity, with the value of tortuosity approaching 1 at upper limits of porosity. Tortuosity also decreased with increase in fiber diameter whereas increase in fiberweb thickness resulted in the increase in tortuosity within the range of fiberweb thickness tested.

An Empirical Equation for Flow Through Porous Media

2005 ◽  
Author(s):  
C. A. Ortega Vivas ◽  
S. Barraga´n Gonza´lez ◽  
J. M. Garibay Cisneros
Keyword(s):  
Reynolds Number ◽  
Porous Medium ◽  
Pressure Drop ◽  
Empirical Equation ◽  
Experimental Methods ◽  
Two Dimensional ◽  
Inertial Effects ◽  
Flow Through Porous Media ◽  
Flow Through ◽  
Porous Medium Model

This study analyses the macroscopic flow through a two dimensional porous medium model by numerical and experimental methods. The objective of this research is to develop an empirical model by which the pressure drop can be obtained. In order to construct the model, a series of blocks are used as an idealized pressure drop device, so that the pressure drop can be calculated. The range of porosities studied is between 28 and 75 per cent. It is found that the pressure drop is a combination of viscosity and inertial effects, the later being more important as the Reynolds number is increased. The empirical equation obtained in this investigation is compared with the Ergun equation.

Effect of Heterogeneity on the Non-Darcy Flow Coefficient

1999 ◽  
Vol 2 (03) ◽  
pp. 296-302 ◽  
Author(s):  
Ganesh Narayanaswamy ◽  
Mukul M. Sharma ◽  
G.A. Pope
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Porous Media ◽  
Pressure Drop ◽  
Characteristic Length ◽  
Flow Coefficient ◽  
Darcy Flow ◽  
Liquid Saturation ◽  
Flow Through ◽  
Heterogeneous Formation

Summary An analytical method for calculating an effective non-Darcy flow coefficient for a heterogeneous formation is presented. The method presented here can be used to calculate an effective non-Darcy flow coefficient for heterogeneous gridblocks in reservoir simulators. Based on this method, it is shown that the non-Darcy flow coefficient of a heterogeneous formation is larger than the non-Darcy flow coefficient of an equivalent homogenous formation. Non-Darcy flow coefficients calculated from gas well data show that non-Darcy flow coefficients obtained from well tests are significantly larger than those predicted from experimental correlations. Permeability heterogeneity is a very likely reason for the differences in non-Darcy flow coefficients often seen between laboratory and field data. Introduction In this paper, we present an analytical method for calculating an effective non-Darcy flow coefficient for a heterogeneous reservoir. The effect of heterogeneity on the non-Darcy flow coefficient is also shown using numerical simulations. Non-Darcy flow coefficients calculated from the analysis of welltest data from a gas condensate field are compared with experimental correlations. Such a comparison allows us to more accurately assess the importance of non-Darcy flow in gas condensate reservoirs. Literature Review As early as 1901, Reynolds observed, in his classical experiments of injecting dye into water flowing through glass tubes, that after some high flowrate, flow rate was no longer proportional to the pressure drop. Forchheimer1 also observed this phenomena and proposed the following quadratic equation to express the relationship between pressure drop and velocity in a porous medium: d P d r = μ k u + β ρ u 2 . ( 1 ) This equation has come to be known asForchheimer's equation. At low Reynolds number (creeping flow conditions), the above equation reduces to Darcy's law. Tek2 developed a generalized Darcy equation in dimensionless form which predicts the pressure drop with good agreement over all ranges of Reynolds numbers. Katz et al.3 attributed the phenomenon of non-Darcy flow to turbulence. Tek et al.4 proposed the following correlation for?: β = 5.5 × 10 9 k 5 / 4 ϕ 3 / 4 . ( 2 ) Gewers and Nichol5 conducted experiments on microvugular carbonate cores to measure the non-Darcy flow coefficient. They also studied the effect of the presence of a second static fluid phase and the effect on plugging due to fines migration. They found that ? decreases and then increases with liquid saturation. Wong6 studied the effect of a mobile liquid saturation on ?. He used distilled water as the liquid phase and water saturated nitrogen as the gas phase on the same cores used by Gewers and Nichol. He plotted ? vs liquid saturation and found that there is an eight-fold increase in ? when the liquid saturation increases from 40% to 70%. He concluded that ? can be approximately calculated from the dry core experiments by using the effective gas permeability. Geertsma7,8 introduced an empirical relationship between ?,k and ? based on a combination of experimental data and dimensional analysis. He noted that the observed departure from Darcy's law was due to the convective acceleration and deceleration of the fluid particles. He also defined a new Reynolds number as ?k??/?, and suggested the following correlation for ? with a constant C (k is in ft 2, ?is in 1/ft). β = C k 0.5 ϕ 5.5 . ( 3 ) For the case of gas flowing through a core with a static liquid phase, he suggested the following correlation: β = C ( k k r g ) 0.5 [ ϕ ( 1 − S w ) ] 5.5 . ( 4 ) Phipps and Khalil9 proposed a method for determining the exponent in a Forchheimer-type equation. Firoozabadi and Katz10 presented are view of the theory of high velocity gas flow through porous media. Evanset al.11 reviewed the various correlations. They conducted an experimental study of the effect of the immobile liquid saturation and suggested a correlation based on dimensional analysis. Nguyen12performed an experimental study of non-Darcy flow through perforations on a synthetic core using air. These experiments showed that non-Darcy flow exists in the convergence zone and the perforation tunnel. Results of this study showed that Darcy flow equations can over predict well productivity by as much as 100%. Jones13 conducted experiments on 355 sandstone and 29 limestone cores. These tests were done for various core types: vuggy limestones, crystalline limestones, and fine grained sandstones. He presented the following correlation: β = 6.15 × 10 10 k − 1.55 . ( 5 ) He also points out that the group ?k? which is the characteristic length used for defining a Reynolds number for porous media, should be proportional to the characteristic length k/ϕ. He developed an approximate multilayer flow model that demonstrates that the departure from the above relation is due to permeability variations. Jones suggested that heterogeneity may be the reason why all correlations involving ? exhibit so much scatter.

Determination of pressure drop for air flow through sintered metal porous media using a modified Ergun equation

2016 ◽  
Vol 27 (4) ◽  
pp. 1134-1140 ◽  
Author(s):  
Wei Zhong ◽  
Ke Xu ◽  
Xin Li ◽  
Yuxuan Liao ◽  
Guoliang Tao ◽  
...  
Keyword(s):  
Porous Media ◽  
Pressure Drop ◽  
Air Flow ◽  
Ergun Equation ◽  
Sintered Metal ◽  
Flow Through

scholarly journals Pressure drop and average void fraction measurements for two-phase flow through highly permeable porous media

2016 ◽  
Vol 94 ◽  
pp. 422-432 ◽  
Author(s):  
N. Chikhi ◽  
R. Clavier ◽  
J.-P. Laurent ◽  
F. Fichot ◽  
M. Quintard
Keyword(s):  
Porous Media ◽  
Pressure Drop ◽  
Void Fraction ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Through

Solvent Flooding Displacement Efficiency in Relation to Ternary Phase Behavior

1972 ◽  
Vol 12 (02) ◽  
pp. 89-95 ◽  
Author(s):  
Ahmad H.M. Totonji ◽  
S.M. Farouq Ali
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Phase Behavior ◽  
Ternary Phase ◽  
Ternary Systems ◽  
Ternary Mixtures ◽  
Displacement Mechanism ◽  
Irreducible Water Saturation ◽  
Experimental Runs

Abstract The chief objective of the study was to exercise control on the system phase behavior through the use of mixtures of two alcohols exhibiting opposite phase behavior characteristics in the alcohol-hydrocarbon-water system involved. Such systems were employed in displacements in porous media to ascertain their effectiveness. Introduction Displacement of oil and water in a porous medium by a mutually miscible alcohol or other solvent has been the subject of numerous investigations. This process, in spite of its limited scope as an oil recovery method, has certain mechanistic features that are of value in gaining an understanding of some of the newer recovery techniques (e.g., the Maraflood* process). The works of Gatlin and Slobod, proposing piston-like displacement of oil and water by a miscible alcohol; of Taber et al., describing the displacement mechanism in terms of the ternary phase behavior involved; and of Holm and Csaszar, defining displacement mechanism in terms of phase velocity ratio, are major contributions in this area. In a later work, Taber and Meyer suggested the addition of small amounts of oil and water (as the case may be) to the alcohol used for displacement, since this helped to obtain piston-like displacements with systems that are usually characterized by the efficient displacement of either oil or water. APPARATUS, EXPERIMENTAL PROCEDURE, AND SIMULATOR PROCEDURE, AND SIMULATOR The procedure employed for determining the equilibrium phase behavior of ternary systems involved the titration of a hydrocarbon-water (or brine) mixture by the particular solvent (pure alcohol, or alcohol mixture) for the determination of the binodal curve, and the analysis by refractive index measurement of ternary mixtures having known compositions for the determination of the tie lines. Since the procedure is valid for strictly ternary systems, its use in this case where essentially quaternary systems are involved would yield the total alcohol content rather than the correct proportion of each alcohol. The ternary diagrams presented should be viewed with this limitation in mind. presented should be viewed with this limitation in mind. The apparatus used for experimental runs in porous media consisted of a positive displacement Ruska pump and a core encased in a steel pipe. Suitable sampling apparatus and auxiliary equipment were employed. Most runs consisted of injecting a slug of the particular solvent into a core initially containing a residual oil (waterflood) or irreducible water saturation, at a constant rate, and then following the slug by water or brine. The effluent samples collected were analyzed for the hydrocarbon, water and alcohol in order to plot the production histories. Complete experimental details and fluid production histories. Complete experimental details and fluid properties are given in Ref. 6. Table 1 lists the properties properties are given in Ref. 6. Table 1 lists the properties of the porous media used. Computer simulations of some of the experimental runs, as well as exploratory simulations, were carried out using the method earlier reported. The method basically consists in the representation of a porous medium by a certain number of cells containing immobile oil (or oleic) and water (or aqueous) fractions into which alcohol is injected in a stepwise manner allowing for phase changes. SPEJ P. 89

Plastic Flow in Confined Porous Media of Complex Contours

1999 ◽  
Author(s):  
Mario F. Letelier ◽  
César E. Rosas
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Theoretical Study ◽  
Perturbation Parameter ◽  
Resistance Coefficient ◽  
Boundary Perturbation ◽  
Bingham Plastic ◽  
Flow Through ◽  
Central Plug

Abstract A theoretical study of the fully developed fluid flow through a confined porous medium is presented. The fluid is described by the Bingham plastic model for small values of the yield number. The analysis allows for many admissible shapes of the wall contour. The velocity field is computed for several combination of relevant parameters, i.e., the yield number, Darcy resistance coefficient and the boundary perturbation parameter. The wall effect is especially highlighted and the characteristics of the central plug region as well. Plots of isovel curves and velocity profiles are included for a variety of flow and geometry parameters.

Determination of the Near-Wellbore Pressure Drop for Dual Casing in Hydraulic Fracturing and Refracturing Applications

2022 ◽  
Author(s):  
Joern Loehken ◽  
Davood Yosefnejad ◽  
Liam McNelis ◽  
Bernd Fricke
Keyword(s):  
Pressure Drop ◽  
Hydraulic Fracturing ◽  
Complex Flow ◽  
Cement Layer ◽  
Natural Rock ◽  
Wellbore Pressure ◽  
Flow Through ◽  
The Difference ◽  
Coefficient Of Discharge

Abstract Due to the increases in completion costs demand for production improvements, fracturing through double casing in upper reservoirs for mature wells and refracturing early stimulated wells to change the completion design, has become more and more popular. One of the most common technologies used to re-stimulate previously fracked wells, is to run a second, smaller casing or tubular inside of the existing and already perforated pipes of the completed well. The new inner and old outer casing are isolated from each other by a cement layer, which prevents any hydraulic communication between the pre-existing and new perforations, as well as between adjacent new perforations. For these smaller inner casing diameters, specially tailored and designed re-fracturing perforation systems are deployed, which can shoot casing entrance holes of very similar size through both casings, nearly independent of the phasing and still capable of creating tunnels reaching beyond the cement layer into the natural rock formation. Although discussing on the API RP-19B section VII test format has recently been initiated and many companies have started to test multiple casing scenarios and charge performance, not much is known about the complex flow through two radially aligned holes in dual casings. In the paper we will look in detail at the parameters which influence the flow, especially the Coefficient of Discharge of such a dual casing setup. We will evaluate how much the near wellbore pressure drop is affected by the hole's sizes in the first and second casing, respectively the difference between them and investigate how the cement layer is influenced by turbulences, which might build up in the annulus. The results will enhance the design and provide a better understanding of fracturing or refracturing through double casings for hydraulic fracturing specialists and both operation and services companies.

scholarly journals Predicting porosity, permeability, and tortuosity of porous media from images by deep learning

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Krzysztof M. Graczyk ◽  
Maciej Matyka
Keyword(s):  
Neural Networks ◽  
Porous Medium ◽  
Porous Media ◽  
Deep Learning ◽  
Lattice Boltzmann ◽  
Good Accuracy ◽  
Two Dimensional ◽  
Empirical Estimate ◽  
Flow Through ◽  
Boltzmann Method

AbstractConvolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($$\varphi$$ φ ), permeability (k), and tortuosity (T). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. The analysis has been performed for the systems with $$\varphi \in (0.37,0.99)$$ φ ∈ ( 0.37 , 0.99 ) which covers five orders of magnitude a span for permeability $$k \in (0.78, 2.1\times 10^5)$$ k ∈ ( 0.78 , 2.1 × 10 5 ) and tortuosity $$T \in (1.03,2.74)$$ T ∈ ( 1.03 , 2.74 ) . It is shown that the CNNs can be used to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between T and $$\varphi$$ φ has been obtained and compared with the empirical estimate.

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