vortex-l  

Re: [Vo]:Question regarding basic solid mechanics and one directional applied stress

R C Macaulay
Mon, 05 May 2008 04:56:26 -0700

Howdy David,
I don't know the answer. Are we discussing earth science and soil mechanics  
separate from solid mechanics?  Nobody knows earth science except geologists 
and Al Gore and they know it all. Just ask one of them.
Soil mechanics is a less than exact science and the approach you have toward 
examining the stresses based on temperature may lead you astray. Sound 
interesting. Some astute geologists at Houston Texas may have more information 
. You may try the University of Houston since they are near to the center of 
the geologists in the petro business.
Years ago I was did some work on gas measurement in west Texas involving CO2 
icing together with a witches brew of H2S. acid, etc. and down hole pressure 
exceeding 10k PSIG. Across Texas we find anomalies in  down hole temperatures. 
Near surface temperatures may be 140 degrees F and drop as depth increases and 
suddlenly increase above 200 F. An interesting study was done on a well near 
Brazoria Texas. An exploratory well was drilled to a final depth of 19-20k feet 
deep with no success. Gosh awful pressures and problems with heat and salt 
water intrusion from nearby Gulf of Mexico.You may try to chase this report 
down at Mobil Oil.

They seem to be having a problem with down hole temperature in the nation of 
Chad. Exxon has some production there. The Chinese are moving in where the 
bullets don't fly. Their biggest problem in production seems to be lightning 
and electric submersible pump motors in the oilwells.
We looked at the problem from a lightning arrestor view and decided there was 
not a solution because of the soil. Strange and weird stuff.
Richard


David Jonsson wrote,

>This is a traditional basic question in solid mechanics and there is nothing 
>special with it.

I am interested in the earth crust and bore holes in it. Gravity is causing 
vertical stress on the crust but it is not obvious if the horizontal stress is 
positive or negative.

One problem is if the crust can expand sideways and thus have a horizontal 
stress or if the geometry only allows isotropic contraction as would be the 
case if a sphere is shrinking. 

If we assume a negative horizontal stress what would the stress be around a 
vertical hole in the ground? The radial stress on the surface of the hole would 
be zero so there would be a gradient on the radial stress from the surface and 
into the rock which is identical to a volumetric force. Volumetric forces cause 
adiabatic heat gradients which means the measured temperature in the bore hole 
is different from that in the rock deeper into the walls of the hole. In order 
to calculate this non heat conducting (adiabatic) heat gradient I need to know 
the potential  function of the displacement of the atoms in the crystals. Since 
silicon dioxide is the dominant component of the crust I will focus on such 
crystals.

There is a bore hole in Poland where the temperature is dropping with 
increasing depth. This would indicate a positive horizontal stress. It can not 
be explained with the dominant theory of heat conduction from the interiors of 
the earth. 

David