Presentation on designing an experiment to calculate permeability of porous medium

Presented by:

Akansha SrivastavaMohita JaiswalArpit GargSharique

Permeability

Permeability is the measure of the soil’s ability to permit water to flow through its pores or voids

Due to the existence of the inter-connected voids, soils are permeable. The permeable soils will allow water flow from points of high energy to points of low energy.

Darcy lawDarcy's Law is a generalized relationship for

flow in porous media. It shows that the volumetric flow rate is a function of the flow area , viscosity, fluid pressure and length of bed.

It may be stated in several different forms depending on the flow conditions.

It has been found valid for any Newtonian fluid.

Darcy’s law equation Q= -KA(dP/dH)/µQ = volumetric flow rate (m3/s).A = flow area perpendicular to L (m2 ).

K = permeability(m2).H = flow path length (m).P= hydraulic head (m).

Continued…

Assumptions

The fundamental premises for Darcy’s law to work are:

the flow is laminar, no turbulent flows.fully developed flow.the flow is in steady state.the fluid should be Newtonian .medium is isotropic

Experimental setupMaterials used50 ml syringeBottleSandWaterScaleBeaker

Experimental ProcedureInsert a half sliced bottle into the open end of

syringe.Add 35.2 cm3 of sand into the setupThen slowly open tap to add water and

maintain a constant pressure head over the sand column.

After steady state is attained measure flow rate at different time intervals.

Experimental setup

OBSERVATION TABLESerial no.

Time interval (min)

Level Of Water (cm)

Flow rate (cm3/s)

1. 2 1.9 29.5

2. 2 2.0 31.1

3. 2 1.8 28.026

4. 2 1.9 29.5

CalculationsTemperature(ambient)=313 kelvinviscosity of water=0.000653 Pasdensity of water= 0.9925 g/cm3 Q(average) =29.5*10^-6 (m3/s )A =2.22*10^-3 (m2 )H =5*10^-2(m )ΔP= 1470 Pascal

Graph of time(x-axis)versus volumetric flowrate(y-axis)

0.5 1 1.5 2 2.5 3 3.5 4 4.50

20

40

60

80

100

120

140

Y-Values

Y-Values

Effect of various parameters on permeability

s.no. Temp(kelvin)

Density(kg/m3)

viscosity(Pa.sec)

Pressure drop(Pa)

Permeability(darcy)

1. 278 1000 0.001520 1470 0.53

2. 293 998.49 0.001 1467 0.354

3. 313 992.25 0.000653 1458 0.23

4. 333 983.13 0.000467 1445 0.168

Graph of permeability(y-axis) vs temperature(x-axis)

270 280 290 300 310 320 330 3400

0.1

0.2

0.3

0.4

0.5

0.6

Y-Values

Y-Values

Axis Title

Axis Title

Result

K= -QµH/(AΔP) Darcy

Permeability Calculated = 0.236 Darcy.

Sources of errorError in scale measurements.Anomaly in time measurements.Sand column may not be completely packed.Tortuous path followed by fluid in sand

column.Material is not homogeneous.

Thank you