The Thermal Movement of Moisture in Soil A. S. M I C K L E Y

A S S O C I A T E A I E E

IT HAS long been known that when a moist soil is subjected to a temperature gradient, the moisture will

have a tendency to move in the direction of heat flow. This phenomenon is of considerable interest in cable heat-ing studies because the thermal conductivity of the earth in the heat field involved will decrease as moisture is lost. It is of like interest in the heat pump using a buried ground coil, where migration has also been observed.

The moisture in the soil is considered to be held in droplets between soil particles. The application of a thermal gradient causes these droplets to move Irom the warmer to the cooler regions. Such movement apparently takes place almost entirely in the liquid phase, and not in the vapor phase, as might at first be supposed. The hy-pothesis is advanced that the thermal gradient causes the individual droplet to distort in shape due to the thermal coefficient present in the value of surface tension. In the process of distorting, the droplet may meet another droplet and the two merge into a single larger droplet. This new droplet will have a tendency to move to the cooler region in the search for a condition of surface tension equilibrium among the complicated crevice system presented by the soil particles. The mathematical expression for this process is on a probability basis, and includes two factors:

1. Amount of distortion, which is proportional to temperature gradient.

2. The probability of meeting another droplet for a given distortion, which is proportional to the difference of the second and fifth powers of moisture content.

Table I. Examples of Moisture Movement Effects

AM = k .m W-(T)'] (1) dx\\F,

is the complete equation, where AM = Moisture lost k — Constant, depending on soil type dT/dx — Temperature gradient Mi — Initial moisture content F= Saturation moisture content

A typical relationship for one soil sample is given in Fig-ure 1. From this it can be seen that the migration is highest at about 75 per cent of saturation.

Electrical utilities, with large investments in under-ground cables, for many years have feared the effects of moisture migration on cable temperatures. In the absence of a means to evaluate this effect, they have limited the temperature of cables and ducts in direct contact with the earth, in the hope that a serious runaway of moisture would be prevented. This temperature limit is usually set at 50 to 55 degrees centigrade.

Digest of paper 49-83 , " T h e Thermal Movement of Moisture in Soil ," recommended by the AIEE Insulated Conductor Committee and approved by the A I E E Technical Program Committee for presentation at the A I E E Winter General Meeting, New Ycrk, N . Y., J anua ry 31-February 4, 1949. Scheduled for publication in A I E E Transactions, volume 68, 1949.

A. S. Mickley is with the Philadelphia (Pa.) Electric Company .

6-Cable Duct Bank

8-Inch Pipe

Maximum heat flow, watts per foot 30 38 Buried depth to center, inches 43 40 Init ial ear th resistivity, degrees centigrade centimeters

per wat t 75 60 Max imum temperature gradient, degrees centigrade per

centimeter 0 .45 1.17 Tempera tu re rise of structure, degrees centigrade

(a) . Neglecting moisture movement 25 .2 35.7 (b) . With maximum moisture movement 2 6 . 0 37 .5 (c). Per cent increase due to moisture movement 3 .2 5 .0

Equation 1 has been applied to the heat field of a buried cylinder for the purpose of providing a method to determine the effect of moisture movement on actual cable problems. The application of the method to two typical examples is given in Table I. Solution of a typical problem of a

Figure 1. Thermal movement of soil moisture — theo-retical curve of surface tension movement plotted against experi-mental data for Barnes loam, sub-stratum soil level

Experimental data are from W. O. Smith's paper, " Thermal Con-ductivities in Moist Soils" Proceedings, Soil Science Society of

America, 1939

MX -dl-d

2 < I

CO CO O

u D H CO

O 2

/

4 o j-

^ι T i

P /

o

■ /

•1 I f

X - T

y

ES" T P Olh IT

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

INITIAL MOISTURE CONTENT m high-tension pipe-type cable system indicates that the temperature rise of the pipe would change only from 36 to 38 degrees centigrade with the most unfavorable migra-tion conditions.

One should not expect that the moisture movement phenomenon discussed in this paper would be applicable at very high temperature gradients. Little is known about the critical temperature gradient, beyond which moisture will migrate until only dry earth remains. The author has had but one experience with this drying-out ef-fect. In this instance the drying-out effect started at 65 degrees centigrade and at a surface temperature gradient of 6.6 degrees centigrade per centimeter, but proceeded in an orderly fashion, with the effective earth resistivity sta-bilizing at a new level approximately 30 per cent greater than the original one.

OCTOBER 1949 Mickley—Thermal Movement of Moisture in Soil 861