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ENPE 313 Introduction to Flow in Porous Media

(Winter 2012)

Lab I Darcys Law ! Per"eability Measure"ent

#b$ecti%e

In this laboratory experiment the permeability of a sandpack will be determined by using

unsteady-state method.

Introduction

Permeability is a property of a porous medium. It is a measure of the capacity and ability of the

porous materials to transmit fluids. This parameter is determined entirely by the pore structure of

the porous medium. The permeability kwas first defined mathematically by Henry Darcy in

1!". The e#uation that relates permeability with measurable #uantities is called Darcy$s %aw&

L

PAkq

=

' (1)

where q * +olumetric flow rate (cm,sec)

A =cross-sectional area of the sample normal to the flow direction (cm)

L * length of the sample in the flow direction (cm)

P * hydrostatic pressure drop (atm)/ * +iscosity of the fluid (cP).

0sing these units in Darcy$s law results in the practical unit of permeability darcy (D). If I units

are used in Darcy$s %aw' qis in m,s'Ain m'Lin m'Pin Pa' / in Pa.s and the units of k arem. 1 darcy * 2.34 x 12-1m.

Permeability can be determined using either steady-state or unsteady-state method. tedy-state

measurement of permeability is usually performed with one-dimensional' cylindrically shaped

samples. In the measurement +arious flow rates of the fluid are recorded as a function of pressuredrop. Permeability is obtained by fitting a straight line to the data points. Theoretically' this line

should pass through the origin.

In unsteady-state method' the pressure difference between the two faces of the sample is

permitted to change gradually with time. 5 so called 6falling head permeameter7 used in li#uid

permeability measurements is shown in 8igure 1.

Darcy$s %aw for the flow dri+en by gra+ity can be written as

( )dV kA ghq

dt L

= = ()

9hereV = cumulati+e +olume of li#uid collected up to time t

a * cross-sectional area of the stand pipe containing the li#uid feed

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h * height of the li#uid column abo+e the li#uid outlet le+el

:; * density difference between the li#uid and air (< density of the li#uid)

g * gra+itational acceleration

8igure 1.12 chematic diagram of falling head permeameter (Dullien' 133)

The solution of =#uation is&

ln o

t

h kA gt

h aL

=

(,)

9hich can be written as&

ln o

t

haLk A gt h

=

(>)

In calculation using I units' ; is in kgm,' and g * 3.1 msec.

The following conditions must be satisfied during the measurement of permeability&

%aminar flow

?o reaction between fluid and the porous medium

@nly single ?ewtonian fluid present at 122A saturation.

&''aratus

The apparatus consists of a sandpack core' a burette (graduated tube)' a stand' and a beaker as

shown in 8igure . Two fluid distributors are used at the two ends of the sandpack to ensure one-

dimensional flow. 5 ruler and a stop watch will be needed to measure the height of the li#uid

column and time' respecti+ely.

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8igure . 5pparatus of Darcy flow test.

Procedure

1. Preparation of the test

The sandpack is 122A saturated with water (by using imbibition method). The tube that

connects the core and the burette is filled with water. The burette is also filled with water to a

certain starting le+el. Before performing flow tests you need to&

Ceasure the height of the outlet of the core.

Ceasure the height of the starting li#uid meniscus.

Ceasure the distance between 2.2 ml and !2.2 ml marks of the burette' to determine

the cross-sectional area of the burette.

8ind the cross-sectional area and the length of the sandpack.

Cake sure that there is no gas bubbles in the tube and burette.

2. Flow tests

1) 5dd water to the burette to 2.2 ml mark (top graduation) with both +al+es closed.

) @pen the +al+e at the outlet of the core.

,) tart to flow the water by opening the stopcock at the bottom of the burette and

simultaneously start the stop watch.

>) ecord time corresponding to different locations of the meniscus in the burette in

increments of ml.

!) Eontinue recording time for one hour or until the burette has drained completely

(whiche+er comes first).

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e'ort

8ollow the =?P= ,1, lab report guideline presented below in the 5ppendix.

In esults and Discussion' your report must contain the followings&

1) Data& Pro+ide your recorded raw data in a table.

) Ealculations& 0se =#uation > to calculate the permeability corresponding to eachrecorded time using the initial height as hoin all calculations. how at least one sample

calculation in I unit system. Ealculate the a+erage of all permeability +alues.

,) Plots and discuss&

Plot ln(hoht) +ersus t on a graph and fit a straight line through the data points.

Ealculate the slope of this straight line.

0se =#. , to calculate the permeability from the slope of the fitted line.

Eompare this +alue to the a+erage calculated earlier. 9hich +alue is more reliableF

>) 5nalysis&

Discuss possible sources of errors in this experiment.

9hat is the relation between the height of the li#uid column and flow rateF

9hat will be the effect of li#uid height on permeability (k)F

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&''endi* ENPE 313 Lab e'ort +uideline

5ll lab reports in =?P= ,1, are to be organiGed under the following headings.

,itle 'a-e Includes course number and title' your names' experiment date' etc.

.u""ary / 5 brief statement of the purpose or obecti+e of the test(s)' the main findings.

Introduction / 5 more detailed description of the purpose of the tests.

Procedure / Describes your test procedure and e#uipment used.

esults and Discussion - The most important part of the report. Present your raw data and

analysis. 9here possible show a sample calculation and then tabulate similar type calculations in

a table. If necessary plot the appropriate graphs corresponding to your data. Discuss your results

and analyGe the sources of error. Point out any unanticipated or unexplainable beha+ior noted.

5d+ance explanations for unexpected results when appropriate.

onclusions and eco""endations / 5 brief statement' describing how the test results'

findings' and analysis meet the obecti+e(s)purpose established at the start of the report.

Pro+ide recommendations for ways to impro+e the experiment.

eerences 5 list of references should be included.

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