WATER DENSITY AND SOILS INTRINSIC
PERMEABILITY
DEPENDENT ON TEMPERATURE
Jurcă ŞTEFANIA-ALINA
West University of Timisoara, Faculty of Physics
300 223 Timisoara, Bulv. V.Parvan 4, Romania
ABSTRACT
The paper presents two applications where the variations of water density
and of the soils intrinsic permeability, respectively, as function of
temperature are studied.
Numerical results, using literature data, graphics and some conclusions
are presented.
Keywords: intrinsic permeability, water density
Introduction
A problem more and more discussed in our days is the pollution with its different forms.
Most met forms of pollution go through by means of water, rather through the pollutants
dissolution in water and through the transport farther in rivers or soils, polluting the ground water.
Because 21,8% from the entire sweet water of the world is contained in ground water
and just 0,34% in rivers and lakes, the rest being mostly snow and ice, is very important the study
of water behavior and its infiltration in soil.
The paper set one’s sights on the determination of intrinsic permeability variation with
temperature for various soils and rocks types, rather of the soils capability to let through the water.
Preliminary are determined the variations of pure and salt water density with temperature
and then is made a comparison between the achieved results.
Theoretical notions
Intrinsic permeability, symbolically represented as ki , is defined being the soil ability to
transmit fluids.
It is calculated with the next formula (1):
ki 
where
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K – hydraulic conductivity
η – dynamic viscosity
ρ – fluid density
Kη
ρg
g – gravitation constant
To calculate the density of pure water dependence on temperature is used the next
formula (2):
ρ a  999,9399  4,216485 10  2  T  7,097451 10 3  T 2
 3,509571 10 5  T 3  9,9037785 10 8  T 4
In nature the water may contain various solutes and for that I shall consider bellow the
salt water.
In practice, for the determination of the salt water density according to salinity,
symbolically represented as S, is used the next approximate formula (3):
ρs  ρ a  A  S 
3
B  S2
 C  S2
where:
 A  8,24493  10 1  4,0899  10 3  T  7,6438  10 5  T 2

7
3
9
4
 8,2467  10  T  5,3875  10  T

3
4
6
2
 B  5,72466  10  1,0227  10  T  1,6546  10  T
C  4,8314  10 4

With those formulas we can calculate the density of brine and pure water for various
values of temperature, considering that S=35 g/l.
For calculation of intrinsic permeability we need the values of hydraulic conductivity for
different soil types and the dynamic viscosity of water for various values of temperature, values
which exist in the literature.
Numerical results
Using the formulas (1), (2), (3) and
Maple 9.5 and OriginPro 7.5 programs I
obtained the next graphic representations:
Figure 1. Graph of pure and salt water
density dependence on temperature
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Figure 2. Intrinsic permeability dependence on
temperature for sand types
Figure 3. Intrinsic permeability dependence
on temperature for two types of rocks
Conclusions
In figure 1. we can observe a considerably difference between the density values of pure
water and of brine in function of the temperature. This fact is observable in the day-to-day life, for
example the sea water doesn’t freeze although the temperature is below freezing, practically the
brine with 35 g/l salinity freezes at -1,91°C. Also the variation of brine density has a prime role in
oceans stratification and in existence of ocean currents what makes possible the existence of
marine biota.
In the figures 2 and 3 we can easy remark the differences between sand types and the
two rocks types, respectively, but most important is that the values for intrinsic permeability
decrease with temperature increase.
Thus, we can make one last observation namely that, irrespective of soil or rock types,
the cold water infiltrates easier than warm water.
References
[1]
[2]
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Jurcă Ştefania-Alina, Lucrare de Licenta: Ecosistemele Lumii.Sisteme morfoclimatice pe
Glob, 2007;
Anca Marina Marinov, Dispersia poluanţilor în apele subterane, Editura Printech,
Bucureşti, 2005