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%.

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.

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 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.

scholarly journals An Improved Instrument for Measuring Filter Rod Pressure Drop

1978 ◽  
Vol 9 (5) ◽  
pp. 283-288
Author(s):  
R.L. Dixon
Keyword(s):  
Pressure Drop ◽  
Needle Valve ◽  
Simple Method ◽  
Automatic Data ◽  
Pressure Drops ◽  
Electronic Pressure ◽  
New Instrument ◽  
Measuring Techniques ◽  
Rate Adjustment ◽  
Definition Of

Abstract A compact, portable pressure-drop instrument that incorporates modern electronic pressure-drop measuring techniques has been designed and built. It includes a built-in laminar-flow calibration standard. The new design offers virtual independence from external capillary standards (and the associated problems of maintaining capillary cleanliness), fast digital readout, potential for automatic data processing, and a simple method of flow-rate adjustment at different filter rod pressure drops. Pressure drop measured with the new instrument meets the CORESTA-recommended definition of pressure drop for filter rods. Data collected on the new instrument show that the average and percent coefficient of variation of pressure drops measured on the new instrument compare favourably with data collected by the previously used standard instrument having mainly a vacuum pump, needle valve and water column manometer.

Frictional Pressure Drop in Micro-Channel

2004 ◽  
Author(s):  
Yasuo Koizumi ◽  
Hiroyasu Ohtake ◽  
Hiroki Takahashi ◽  
Yoshiaki Ohno
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Friction Factor ◽  
Frictional Pressure Drop ◽  
Turbulent Transition ◽  
Friction Factors ◽  
Turbulent Flow Regime ◽  
Form Pressure ◽  
Laminar And Turbulent Flow ◽  
Flow Through

The friction characteristics of water in a sub-millimeter scale channel were investigated experimentally. The friction factors and the critical Reynolds number were measured using water flow through circular tubes with diameters of 0.5, 0.25 and 0.17 mm. The experimental results show that the measured friction factor for water agreed well with the conventional Poiseuille (λ = 64/Re) and Blasius (λ = 0.316 Re−0.25) equations in laminar and turbulent flow regime; the laminar-turbulent transition Reynolds number was approximately 2300 for diameter 0.5 mm. For diameter 0.25 mm, the friction factor evaluated by the form pressure drop also agreed well with the Poiseuille equation. For diameter 0.17 mm, the measured total friction factor was close to the Poiseuille prediction.

Determination of Forchheimer Term in Porous Media Consisting of Obstacles of Different Sizes

2012 ◽  
Vol 594-597 ◽  
pp. 2537-2540
Author(s):  
Ren Xing Liu ◽  
Akira Nakayama ◽  
Xiao Lan Haung
Keyword(s):  
Porous Media ◽  
Numerical Models ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Reasonable Estimate ◽  
Pressure Drops ◽  
Pressure Fields ◽  
Definition Of ◽  
Average Size

As a sequel to the study in determining the permeability of the porous media composed of obstacles of different sizes, exhaustive numerical calculations were conducted using the same two-dimensional numerical models of square rods as in the previous study. The models consist of collections of square rod obstacles of two-, three-, four- and five-different sizes. Computations were carried out to reveal the details of microscopic velocity and pressure fields. There results are integrated to find the macroscopic pressure gradients for collections of multi-sized obstacles. The Ergun type general formula has been proposed along with a definition of an effective average size, which, when substituted into the formula, yields a reasonable estimate for the macroscopic pressure drops in multi-sized obstacles.

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