Institutt for petroleumsteknologi og anvendt geofysikk - NTNU
Institutt for petroleumsteknologi og anvendt geofysikk - NTNU
Institutt for petroleumsteknologi og anvendt geofysikk - NTNU
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29<br />
( )<br />
1<br />
2<br />
1<br />
2<br />
ln<br />
1<br />
ln<br />
v<br />
v<br />
k<br />
T<br />
T<br />
−<br />
−<br />
=<br />
or<br />
1<br />
2<br />
1<br />
1<br />
2<br />
−<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
=<br />
k<br />
v<br />
v<br />
T<br />
T<br />
From the ideal gas law<br />
pv = RT<br />
1<br />
1<br />
1 RT<br />
v<br />
p =<br />
2<br />
2<br />
2 RT<br />
v<br />
p =<br />
2<br />
2<br />
2<br />
1<br />
1<br />
1<br />
T<br />
v<br />
p<br />
T<br />
v<br />
p<br />
=<br />
2<br />
1<br />
1<br />
2<br />
2<br />
1<br />
T<br />
T<br />
p<br />
p<br />
v<br />
v = 1<br />
2<br />
1<br />
1<br />
2<br />
1<br />
2<br />
1<br />
2<br />
−<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
=<br />
=<br />
k<br />
v<br />
v<br />
v<br />
v<br />
p<br />
p<br />
T<br />
T<br />
k<br />
k<br />
p<br />
p<br />
T<br />
T<br />
1<br />
1<br />
2<br />
1<br />
2<br />
−<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
=<br />
From<br />
1<br />
2<br />
1<br />
1<br />
2<br />
−<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
=<br />
k<br />
v<br />
v<br />
T<br />
T<br />
and<br />
k<br />
k<br />
p<br />
p<br />
T<br />
T<br />
1<br />
1<br />
2<br />
1<br />
2<br />
−<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
=<br />
we obtain<br />
k<br />
k<br />
k<br />
p<br />
p<br />
v<br />
v<br />
1<br />
1<br />
2<br />
1<br />
2<br />
1<br />
−<br />
−<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
=<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
or
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