On Wed, Mar 9, 2016 at 2:07 PM, Lubomir I. Ivanov <[email protected]>
wrote:
>
> the source which wasn't consistent was the helium experimental data:
> https://shareok.org/bitstream/handle/11244/2062/6614196.PDF?sequence=1
>
> (in-document page 108).
Ok. So what I would suggest doing for that data is to actually do a
least-square fit of *both* of those temperatures together.
That should do a fit right in between. As it indeed does:
​which seems to be a simple and reasonable approach to get a line that goes
in the middle of the 273K and 323K data.
It goes all the way up to 700 bar, because that's what the source does.
With R, that gets me the virial coefficients of
p1 4.87320026468e-04
p2 -8.83632921053e-08
p3 5.33304543646e-11
and the plot doesn't look that far off what we have now.
Patch against the previous R script attached, if people want to verify
this. Because it *would* be good to have somebody sanity-check my
calculations..
Linus
subsurface-core/compressibility.r | 33 ++++++++++++++++++++++++++++++++-
1 file changed, 32 insertions(+), 1 deletion(-)
diff --git a/subsurface-core/compressibility.r
b/subsurface-core/compressibility.r
index 15aca6ea27c9..05784dd3a790 100644
--- a/subsurface-core/compressibility.r
+++ b/subsurface-core/compressibility.r
@@ -39,7 +39,6 @@ o2 = c(0.9994, 0.9968, 0.9941, 0.9884, 0.9771, 0.9676,
0.9597, 0.9542, 0.9560, 0
n2 = c(0.9998, 0.9990, 0.9983, 0.9971, 0.9964, 0.9973, 1.0000, 1.0052, 1.0559,
1.1422, 1.2480, 1.3629)
he = c(1.0005, 1.0024, 1.0048, 1.0096, 1.0191, 1.0286, 1.0381, 1.0476, 1.0943,
1.1402, 1.1854, 1.2297)
-
options(digits=15)
#
@@ -76,3 +75,35 @@ summary(hefit)
new = data.frame(x = seq(min(x),max(x),len=200))
lines(new$x,predict(hefit,newdata=new))
+
+#
+# Raw data from VOLUMETRIC BEHAVIOR OF HELIUM-ARGON MIXTURES [..]
+# T=323.15K (50 C)
+p323atm = c(674.837, 393.223, 237.310, 146.294, 91.4027, 57.5799, 36.4620,
23.1654, 14.7478, 9.4017, 5.9987, 3.8300,
+ 540.204, 319.943, 195.008, 120.951, 75.8599, 47.9005, 30.3791,
19.3193, 12.3080, 7.8495, 5.0100, 3.1992)
+
+Hez323 = c(1.28067, 1.16782, 1.10289, 1.06407, 1.04028, 1.02548, 1.01617,
1.01029, 1.00656, 1.00418, 1.00267, 1.00171,
+ 1.22738, 1.13754, 1.08493, 1.05312, 1.03349, 1.02122, 1.01349,
1.00859, 1.00548, 1.00349, 1.00223, 1.00143)
+
+
+# T=273.15 (0 C)
+p273atm = c(683.599, 391.213, 233.607, 143.091, 89.0521, 55.9640, 35.3851,
22.4593, 14.2908, 9.1072, 5.8095, 3.7083,
+ 534.047, 312.144, 188.741, 116.508, 72.8529, 45.9194, 29.0883,
18.4851, 11.7702, 7.5040, 4.7881, 3.0570)
+
+Hez273 = c(1.33969, 1.19985, 1.12121, 1.07494, 1.04689, 1.02957, 1.01874,
1.01191, 1.00758, 1.00484, 1.00309, 1.00197,
+ 1.26914, 1.16070, 1.09837, 1.06118, 1.03843, 1.02429, 1.01541,
1.00980, 1.00625, 1.00398, 1.00254, 1.00162)
+
+p323 = p323atm * 1.01325
+p273 = p273atm * 1.01325
+
+x2=append(p323,p273)
+he2=append(Hez323,Hez273)
+
+plot(x2,he2)
+
+hefit2 = nls(he2 ~ 1.0 + p1*x2 + p2*x2^2 + p3*x2^3,
+ start=list(p1=0,p2=0,p3=0))
+summary(hefit2)
+
+new = data.frame(x2 = seq(min(x2),max(x2),len=200))
+lines(new$x2,predict(hefit2,newdata=new))
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