VideoPoints

• ••• • •• • ••••• • •
GEOL7324-Rock Physics - ThursOct14
Help Tour
© Distribution of this video is restricted by its owner
Transcript ×
Auto highlight
Font-size
00:01 this conference will now be reached. conference will now be recorded. All
00:07 , so this is where we were time we were talking about the greatest
00:11 discovery of all time. That they a Nobel prize in geophysics. I
00:18 would have won it for the mud line and the great revelation. The
00:24 surprise was that tickets trend for sand which was a peer. Where is
00:36 ? There? It is. so fiddle line to pick its sand
00:42 . This is what graduate students We, you know, have to
00:46 every point there, fit a line it. And uh where were
00:56 And got that? And it was on the mud rock trend. It
01:02 out that sand stones plot in the of the mud rock line. If
01:08 very clean, by clean, I courts, primarily courts. If they're
01:15 and porous and dominated by aspect ratios the order of 1/10 they fought slightly
01:25 the line. If they're felt static a little bit of carbonate or dirty
01:34 clay, they could plot on or the line. And the more
01:39 the more feldspar, the further above line it will pull you uh keep
01:45 mind these are brine saturated sand which is going to be very important
01:50 what we're going to see is when add gas to a sandstone, we're
01:55 to drop the D. P. . S ratio below the mud rock
01:58 . So the mud rock line gives a very good background expectation and that's
02:04 it was important. And in fact I came up with the mud rock
02:08 , I was thinking about a I was thinking about what is the
02:13 , a video response that I should from seismic data and how to hydrocarbons
02:22 from that background response. So, we were, I was working in
02:28 gulf of Mexico at the time, dissertation data was from the gulf coast
02:34 in the Gulf of Mexico three of dominant with all minerals our courts,
02:43 and soft. And it turns out all three of those fall on the
02:48 rock line and in fact feldspar as well. So there's not a lot
02:56 on unless you've got a cal Karius or a limestone will pull you above
03:04 line or if you have hydrocarbons will you below the line. So this
03:09 why it was important. This is I got used and I would like
03:13 point out that the reason it waited me to come along to have this
03:25 is because I had the data early . So as the data was trickling
03:33 , I was forming these ideas with , without being at the bleeding edge
03:39 the data pushing the data at the extremes and grabbing every data point I
03:45 and trying to figure out what was on. And I would not have
03:50 to this realization early on. And became a fundamental basis for a lot
03:57 the video analysis that was done and lot of the hydrocarbons that were found
04:03 primarily on the deviation from the mud line. Uh These were some of
04:11 early data points I have. These full wave form sonic data. Uh
04:17 are gulf coast data and you notice fly below the mud rock line.
04:24 It will see why later. This a paper that came along at a
04:32 , say some of the first full form sonic data that slumber shape
04:38 And you notice a lot of the are right on the mud rock
04:41 but there is some tendency to plot below the line. So we'll come
04:46 and we'll see why that can This was some of my dissertation
04:54 it was frio formation and there was lot of scatter in these in these
05:01 , but you know pretty much right the mud rock line, with the
05:05 of some points here, which plotted the line. It turned out that
05:11 had some free gas saturation in that . These were laboratory measurements and we
05:25 Iraq Physics lab at Arco and basically together all the lab measurements we had
05:34 these were in water saturated sand And you can see that as a
05:41 , if you knew nothing about the , if you just knew it was
05:44 sandstone didn't know anything about the You would see that you pretty well
05:49 along the line. So, sand have very similar V. PBS
05:54 Two shells. Remember pickets trend 1.6 1.7. Well up here, that's
06:02 kind of the PBS rates that we . But down here, look at
06:06 B. P. B. Ratios you're getting and these are in
06:09 stones. Right? So five More or less there be PBS gration
06:16 five. And as I said, time I've seen v. PBS ratios
06:21 high as 40 in the very shallow marine sediments. Okay, so
06:31 they're scattered. That's fine. Later we'll understand that that scatter later
06:36 we'll be able to predict very precisely the B. P. V.
06:41 ratio will be if we know Remember all we know at this point
06:44 the point is that these are sand . As I said, uh If
06:49 have some carbonate in the, you , some carbonate cement, it can
06:53 you up if it's very clean, can pull you down. No rock
07:03 experimental data set would be complete without on Maria stand stone. And so
07:11 had a few measurements on water saturated sandstone. This was these are all
07:16 same sample at different pressures and here's mud rock line and bury a sandstone
07:23 very clean sandstone was right on the rock line except at very low
07:28 It goes above the mud rock Okay, that's something else I had
07:33 spoken about when I was talking about pulls you above the line. Uh
07:38 show you this later. I'll prove to you later that if I have
07:42 filled very flat pores, it will you an anomalous li hai V.
07:48 . So oil fields or water filled pores uh like fractures give you an
07:55 high V. P. S. . Whereas gas filled fractures give you
08:00 abnormally low PPB S ratio. And what we see. Uh You
08:06 these are measurements on the same sample different pressures. This is dry now
08:10 , it's not oven dry, it's dry. But the b.
08:15 s. ratio was significantly lower. 1.5 and it's independent of pressure.
08:23 in the water saturated rock, the . P. S. Ratio is
08:28 pressure dependant how it's moving you up down the line or above the line
08:34 you get to really low pressure. in the guest or the dry sand
08:41 it doesn't matter what the pressure You have a low P.
08:44 P. S ratio. So we're to try to understand that why the
08:48 in behavior between water saturated sand stones dry sandstone. Now we got a
08:57 of verification from around the industry and was some work published by chevron and
09:07 . These are the guys that first a video. The first paper on
09:12 analysis was for most stranded at So they were very interested in what
09:17 V. PBS ratios were. So made a lot of measurements. They
09:22 laboratory measurements, log measurements across all . And they also had measurements and
09:28 stones um you know, remarkably close the mud rock line. Especially these
09:36 high B. P. V. . Ratios measured cross hole in the
09:41 days. We didn't have logs at very low velocities. We didn't have
09:47 wave velocity logs. Uh So but use cross hold measurements and very much
09:54 on the mud rock line. I have people uh bump into me in
09:59 and uh tell me that uh mud line was working for them. It
10:06 kind of funny, you know, introduce you, you meet somebody in
10:10 airport as soon as I mentioned my , they say oh yeah we use
10:14 line and it works pretty pretty So it became pretty ubiquitous. This
10:22 more data from Chevron. And here used a multi component seismic data from
10:30 component data. If you have P. Sections and Bs sections,
10:34 hard to measure BP and it's hard measure VFC from seismic data. How
10:40 you measure VP? Well, you uh interval velocities right from from normal
10:45 out. That's usually pretty inaccurate and low resolution. On the other
10:52 if you have can pick horizons on P wave section and pick horizons over
10:59 same depth interval if you could get in and make sure you're picking the
11:04 event on the p wave section and wave section, just from the travel
11:09 ratio that directly gives you the P. V. S ratio.
11:13 I get the shear wave travel time top to bottom of the layer and
11:17 few wave travel time from top to of the layer. So from the
11:21 I can directly measure the V. . V. S ratio. So
11:25 what Chevron did here and they had number of layers where they had reflections
11:30 top and base. You see these interfaces that will give you good
11:35 And they were able to get the on the P wave section and on
11:39 share wave section and measure the P. V. S ratio.
11:43 it was precisely what the mud rock would have predicted. Okay now,
11:54 we looked at the porosity and clay dependence of BP and Ds.
12:03 we saw in the free information I these the Eastwood equations because he's the
12:08 that did this regression. And and got nice relationship between buying clay ferocity
12:18 VPN Bs. And these relationships were similar to laboratory relationships that society came
12:27 with at stanford uh in fact messiahs uh was from a wide variety of
12:37 that were competent enough to core plug make laboratory measurements on. So in
12:46 they're very different shells. These are formation uh shells and silt stones and
12:53 sand stones etcetera, we came up these relations and these are more like
12:59 well liquefied shells and uh you know similar relationships. Now given these relationships
13:10 could then as a function of volume and ferocity. You can then plot
13:16 V. P. V. Relationship. And so that's one of
13:21 homework assignments is to do that. use these two sets of equations And
13:28 varying porosity over a reasonable range and volume of clay from 0 to
13:35 See where these uh equations plot on D. P versus V.
13:41 Cross plot. So that's your exercise . Uh You can do it for
13:48 courts pure clay in 50 50. be clave zero the clay of one
13:55 the clay of 10.5. So you have three V. P.
13:59 S. Curves for the for the of formation and three Bp versus
14:04 S. Curves for to side as measurements. And what you'll get is
14:13 plot like this. Um And I , okay, these are too
14:19 All right. And so the mud line is the black curve. So
14:25 you're very porosity for zero volume McLay is putting you on the mud rock
14:33 and you increase the porosity here are ferocity for Volume McLay of one and
14:43 still puts you on the mud rock , this is some points are
14:47 some points are below. But overall you look at the full range of
14:52 and volumes and volumes of play. puts you on these lines. So
14:58 just want to see you generate these but the answer should look something like
15:08 . Now understanding these V. PBS . I mean knowing where the minerals
15:16 on these lines is important. So plots there, course plots there.
15:25 Well of course and size equations plots , that would be zero porosity
15:33 This would be zero porosity clay. end of those lines. So here
15:38 some uh measurements on minerals and it be worthwhile to see where these oh
15:45 on a VP VS. Bs. . Also we have some values for
15:52 that have been inferred. These are to 100% clay. Um So anyway
16:01 p. P. P. Ratios for Claes. So it be
16:05 to see where these clot relative to mud rock line. So we could
16:10 some expectations here since rocks are aggregates mineral grains, we expect the velocity
16:19 a highly liquefied, low porosity rock depend strongly on the velocities of the
16:25 . So as we go towards zero we should go towards these points we
16:36 expect velocities of unconsolidated rocks with higher to be weakly dependent on the
16:43 Philosophy more dependent high porosity more dependent the ferocity degree of lift ification
16:52 As a result though, on a . P. B. S cross
16:56 . If I have a monumental alec and it's a water saturated rock,
17:03 expect one endpoint uh huh. To that of the mineral. Right?
17:11 the other endpoint should approach water. should show a V. S.
17:15 towards zero And the VP trending towards P wave velocity of water. And
17:22 pretty much what we have over It's not precisely water but it's in
17:27 vicinity of water. Water is This intercept is 1.36. So in
17:33 the curve has to bend To be for at 100% porosity, right?
17:39 has to them. Okay, so could look at these trends where we
17:52 the composition better. So this is V. P. B.
17:56 Relationship for clean court sandstone. There's such thing as 100% coarse Sandstone.
18:04 ? Or if they exist there are few. So what we did is
18:09 took sand stones that were 90% or courts. That still means there's They're
18:16 , you know, clay, if structural 10% clay could still have a
18:20 impact on velocity. But anyway, narrow things down as far as we
18:26 . And in fact, if you a regression on composition, you could
18:30 uh take, you know, You then extrapolate to 100% courts. That's
18:36 what was done here. What was here was just fit a line to
18:41 clean sand stones. Right? In , that's what we were allowed to
18:45 . In fact, internally, we use these trends. So these have
18:52 come to be known as the Greenberg trends which are also used quite a
18:58 in industry to predict your way We didn't use these trends. We
19:03 regressions against composition. And so the we had were proprietary and never
19:11 So they're not out there in the , but it's something that could be
19:15 relatively easily, more or less taking envelope of these lines. So this
19:21 sam stone. Uh And it's a relationship. And we're going to come
19:29 and we're going to try to understand this is a linear relationship. Although
19:34 think you can see it's trying to back, it's trying to swing back
19:38 water here. All right. But most of the range, it's
19:43 And in the end, our explanation it's linear because it's fortuitous. Uh
19:51 I'll try to explain that a little more as we come back. It
19:54 to do with what is the P. S ratio of courts versus
19:58 V. P. B. S for a dry sand pack. Um
20:03 the other hand, limestone where the . P. S ratio of the
20:08 is very different from the V. . V. S ratio of a
20:12 pack of rounds calcite grains. What is limestone swings non linear.
20:21 for high velocity lime stones, pickets is avi PBS ratio at 1.9.
20:27 actually works better then the polynomial fit all the data. So I like
20:33 use pickets trend if I'm in liquefied , it's only if you get too
20:39 marine sediments. Where you're talking about limestone is those kinds of things,
20:46 , etcetera. Where you have to about this curvature here. So I
20:51 typically break the limestone into two types limestone. I use pickets trend and
20:58 abide limestone, I then used the that and again you can see is
21:05 to swing back towards water there. so you could ask yourself why is
21:10 linear for sandstone through most of of . But there's this distinct bend,
21:16 for limestone. Um I think we'll that as we look into this a
21:22 bit more deeply. And uh this the line we had for Pew pure
21:30 . Now, what is a pure ? Um Obviously no shell is 100%
21:39 mineral. Right? And so we elude. Somehow they let us publish
21:43 idea that you really if you're trying predict the velocities from volumes if you've
21:51 your volume of clay mineral correctly, should be using a pure clay
21:57 And so we drew a hypothetical play as just being the envelope of these
22:02 there. Uh And that's as far we were allowed to do. We
22:07 never allowed to actually publish what that was. And here's the line for
22:15 . The dolomite data, we had uh the Dolomites we had were significantly
22:24 V. P. V. Ratios than uh pickets trend. So
22:28 might want to compare what this equation vs Pickett, who predicted 1.8 for
22:35 for double line. Okay, so uh flooding all of these points on
22:45 . B. P. D. versus BP cross plot. Some people
22:49 to uh use a B. D. S versus P. Wave
22:53 cross plot. I kind of like because it's a proxy for death because
23:00 the P. Tends to increase with . So deep rocks should be doing
23:05 , shallow rock should be doing And there's a lot to be learned
23:10 this diagram. First of all notice the gas damn D. P.
23:17 . S ratio is invariants. I'll back. I'll prove that to
23:22 I'll show you measurements, um Dry sounds and also we'll do things like
23:28 substitution and predicted the PBS ratios for sands. And you see they're independent
23:35 the velocity, low velocity gas civil oV PBS high velocity gas sands
23:41 a low V. PBS. On other hand, the brine, saturated
23:47 behave differently. Shallow. We see strong dependence of the D.
23:52 D. S ratio on the Wave velocity as we get as we're
23:58 and getting deeper. The V. . V. S ratio has dropped
24:03 . Um until we become fully Then when we're let me say,
24:09 identified when you were in well lit rocks. The little logic effect,
24:14 changes in V. PBS, doodle can be greater. Then the change
24:20 B. P. B. S the hydrocarbon. So, for
24:23 here Gayle sent to the higher the ratios than sand stones. More so
24:31 gas sands are, the B. . V. S ratio is
24:35 So I have an over print of effects on top of fluid effects.
24:41 this makes fluid detection in these kinds environments very tough. I could have
24:47 beautiful HBO anomaly. HBO would show where the anomalous Lobi PBS ratios
24:55 That could be due to a brine sandstone. In fact, studies have
25:00 Allen and petty in their A. . O. Book showed that the
25:04 common false Avio result where you have false positive Avio indication, the most
25:12 results or the most common reason for false positive is clean brine saturated sandstone
25:21 these clean sand stones have a lower . PBS ratio than the shells.
25:29 that effect is actually bigger than the effect in the sandstone. So,
25:33 well, at the five rocks, careful, the PBS could be a
25:38 with ology indicator. In fact, been surprised at how useful Fabio is
25:44 reservoir characterization, predicting reservoir properties. huh. I can't really won't get
25:53 why that was so surprising in But if you take my dhe course
25:57 semester, we'll talk at length about reliability of HBO attributes, etcetera.
26:11 , now there's something else that pulls below the mud rock line and that
26:15 uh organic matter in hydrocarbons in the . All of the none of these
26:24 here, sorry. None of these . And none of the values in
26:28 mud rock went line where organic and it's hard to separate the effect
26:34 the organic matter directly in the effect hydrocarbons directly, But the net result
26:40 the two is Shale reservoirs tend to an abnormally low BPBS ratio. What
26:48 would compared to what you would expect 100% frying saturated shale. Also,
26:55 you take your 100% brine saturated shell predict uh using fluid substitution as well
27:03 later in the course, predict the trend you would have for gas
27:09 Uh the the PBS ratios we actually tends to be intermediate between those and
27:17 when we talk about gas meant equations fluid substitution, hopefully we'll have an
27:23 as to why you don't get the gasman effect in shells. Even coals
27:36 a well defined the PBS relationship. so we have a trend for cole's
27:42 tried using uh this cold strand to shear wave velocities in organic shells.
27:52 we found that this Schultz coal trend not quite right for the organic matter
27:58 shells. And so we have a separate trends for the organic matter in
28:04 , but that, you know, covered that last semester in our unconventional
28:10 rock physics class. Uh I'm not if we'll have time to talk about
28:16 too much this semester. Even So here we had toughs in Oregon
28:27 uh toughs at a nuclear waste Um and similar trans there. Now
28:38 VPs relationships are quite different from the density relationships. Remember we have all
28:46 different VP porosity or VP density transforms wildly. Gregory and Garner Rayburn Hunt
28:54 would like equation critical porosity model, ? We have all these different equations
29:00 any equation you use, there's always lot of scatter around that equation.
29:06 equation you use to transform velocity to is very locality dependent. It depends
29:14 all the things we talked about all different factors, uh, poor
29:21 um pressures, etcetera. Um what find is the V. P.
29:27 . S relationships tend to be pretty and the deviations we get in a
29:35 mythology. The deviations we get are small. So the V.
29:41 V. S relationships are more The big swinger in these relationships.
29:47 big swingers are hydrocarbons tend to lower V. P. V. S
29:54 pressure ferocity. Things like that move up and down the line. They
29:58 move you off the line very much the exception of fractures, very flat
30:04 filled fractures, we'll give you an lee, high ppd s ratio.
30:12 . But based on these trends, what we find is that with ology
30:19 is best at high velocity. So our little ology discrimination and hydrocarbon effects
30:28 best at low velocities. And the between gas and brian is very
30:35 high velocities. So this was an data set uh that where we had
30:47 amazing sonic log data these days. data, it was an experimental sonic
30:53 tool that was developed by a french Elf Aquitaine. And they actually had
31:01 receivers. So they were able to very accurate velocity. So it was
31:07 very interesting data set. And these measurements they made in the paris basin
31:13 we've got different mythologies. So we've sand stones and shells and they're plotting
31:21 along the mud rock line here we've lime stones and we've got clean lime
31:28 that fought on the limestone line. is pickets limestone line. Uh We've
31:34 Dolomites. They fought in between just Pickett found you have some lime stones
31:40 flat in between. And I would these are sandy or Shelly limestone,
31:45 ? Clay And courts will pull the . P. B. S.
31:49 down. So they are essentially indistinguishable dolomite. So if you're looking for
31:54 dolomite reservoir, you may wind up a Shelly limestone. Um But one
32:00 interesting thing. Salt. These are salt values and they're right on the
32:07 rock trend, which is kind of in the gulf of Mexico. All
32:15 now remember there is a 1 to relationship between the V. P.
32:19 . S. Operation, one person's . So the same kind of plot
32:23 showed before uh can be uh plotted terms of Hassan's ratio versus P wave
32:32 and a favorite thought uh that people to use this cuisines ratio versus P
32:37 impedance. Anyway, the same exact can be drawn. This is from
32:43 and Pettis. Uh book a video . Um they give a range for
32:49 sands. I had a line uh know, 1.5 but but those were
32:55 clean guests. And if you have guests and you could actually have higher
33:01 since ratios. Okay, so these the single length ology lines,
33:11 The ones we've looked at limestone. , Singer stone shell. Uh
33:16 Most we could just use a simple equation. If we want to include
33:20 velocity lime stones, we have to non linear. But you could use
33:25 be PBS equals 4.9. If you're high velocity limestone. So you're going
33:31 need these equations for your exercises, come back to that. But I
33:41 to try to understand what's going on try to understand why we have this
33:50 line that we do. And try understand whether we should be on the
33:54 rock line below the mud rock line slightly above it. And a place
34:00 start is with dry stand stuff because don't have the complication of the
34:06 And so these are laboratory measurements in sand stones. And they give a
34:14 . p. v. s ratio essentially 1.5, which is about a
34:19 ratio .1. So that's pretty typical dry rocks. And by inference,
34:24 we talk about gasses, uh, substitution, that's what we would expect
34:31 . You know, gas saturated If we're shallow with the dry
34:35 we should expect similarly. PBS ratio we have in dry sand stuff.
34:42 , that is a starting point for understanding. But why why should this
34:49 PBS ratio be so constant to dry stones? Well, let's think about
34:57 different regimes here. We've got well the five rocks and we have poorly
35:03 rocks. Remember we said that as get go towards zero porosity, we
35:09 approach courts. So courts is somewhere here. So going towards courts makes
35:17 . And As velocities go to Uh, you know, the
35:27 the velocity of air, say shear velocity of zero P wave velocity virtually
35:34 . Not quite remember. Sound travels air, right, But you expect
35:40 go towards 00. So the in are kind of to be expected.
35:47 you know why not a line in . But let's actually talk about what
35:53 packs will do here. And then talk about what crack solids do up
35:59 . So let's talk about sphere We've done these, we've looked at
36:03 , these are different packing. We the most poorest packing. The loosest
36:09 . Simple cubic. We have a close path face centered cubic. These
36:15 both very dense packing. And we calculate using physics, if we have
36:25 regular packing like this, of uniform , spheres of the same size,
36:32 the math becomes relatively easy. And have equations that will tell us what
36:37 V. P D. S ratio the sphere pack should be. As
36:42 vary the grain Hassan's ratio. And at the range of persons ratios we
36:47 here, we have no no mineral a negative response ratio. So we
36:53 the full gamut from zero where I'm Square Root of two. Uh all
37:00 way to .5. All right. what you find is that as the
37:09 Parsons ratio gets lower the range of pack, Hassan's ratios becomes very
37:17 In fact, what is a grain ratio? .5, that would be
37:21 liquid bubble. So, so, I could have uh grains that are
37:28 almost liquid. Right? Almost I still have a low V.
37:34 . B. S. Right, here. So, what we find
37:40 that for dry sphere packs? What I mean by a dry fear pack
37:47 liquids. Right? These are almost . But they have Aaron between
37:52 right? The liquid droplets or perfect . And they're they're in a regular
37:58 with Aaron between them. Very But even that you would expect that
38:04 give you a V. P. . S. Ratio. Uh
38:09 Hi uh response ratio. Right. did that act like a liquid?
38:14 in fact this is what the spirit equations give you. So no matter
38:19 I do, no matter what my is. The sphere pack has the
38:25 V. P. V. Ratio. Remember these can say for
38:28 these could be calcite grains. Castlight a d. p. v.
38:33 . ratio of 1.9. Maybe I'm here someplace my my beer pack of
38:40 grains still has a low B pediatrician below 1.5. So maybe it's not
38:49 that these uh lose sediments that are like spear packs have Lovie PVS
38:57 So maybe I could understand this And remember court says the low
39:05 P. S. Ratio. And then start at the other extreme and
39:11 to work down from the courts Oh by the way before we do
39:20 we could do some experiments and we say what does what would low aspect
39:27 do to the D. P. . S ratio. So I have
39:31 dry line which is a v. . b. s. ratio.
39:35 . I've got dry fan stone measurements a variety. These are the open
39:41 here at high pressure and low pressure they're right on Constantly PSS ratio at
39:51 . Now I'm going to take this dry rock and I'm going to heat
39:58 very hot and then I'm going to it very fast. I'm going to
40:04 it. And so you have a of thermal expansion and contraction. And
40:09 you do that, you crack the , you introduce micro fractures. So
40:15 happens is you lower the velocity if lower V. P. And
40:19 S. But look, it just you the heat cycled experiments that have
40:24 fractured, move you down the trend . Still have a low b.
40:32 . b. s. ratio So in a gas saturated rock,
40:38 gas penetrated Iraqi air is a you know, fully gas that traded
40:44 where you have a very compressible gas air. Uh huh, adding micro
40:50 . Doesn't change the V. V. S ratio. Therefore opening
40:54 closing. Microfractures won't change the P. B. S ratio.
40:59 changing the pressure, won't change the . P. B. S.
41:06 . Okay then we could start with appear and we could add microfractures
41:14 So we could do, you these are complicated equations but actually it's
41:20 a matter. It's just complicated Very complex equations, but easy equations
41:28 that sense. So it's easy to up and you could compute as you
41:37 more and more ferocity and we're in case we're using Iraq with an aspect
41:45 distribution and particular rock was Boise stance just to have a representative range of
41:54 ratios uh for a stamp down and add more and more, greater and
42:02 concentration of these aspect ratios. And see that it doesn't change the
42:09 P. D. S ratio very . You have to get to extremely
42:13 concentrations in order to lower the P. V. S ratio somewhat
42:20 pretty well constant. So what can conclude courts as the VP administration at
42:26 cracked courts has a V. V. S ratio 1.5. Low
42:31 ratio courts. A lot of that has a V. P.
42:36 S ratio. At 1.5 sphere packs a V. P. V.
42:41 ratio 1.5. And so our argument that the reason that this is a
42:47 line is the fortuitous fact that courts spear packs have a very similar
42:54 PBS rations. Had my grain bin . I would this line would have
43:00 to ban from a low V. ratio for a spear pack of
43:06 It would have to veer off towards calcite point. All right, so
43:12 dry line been a line as opposed a curve mm then will help explain
43:24 are fully brine saturated line is what is, is a line.
43:32 So that's what I've got for Do check to see if the recordings
43:39 working for you. Report back to one way or the other.
43:43 it worked. No, it's at one of you let you know it
43:46 . So I know you're getting it we don't have to deal with it
43:48 the last minute. It was a work. Okay. Yeah, I
43:53 working for me. Oh, Great. Okay, Good.
43:58 uh, that was an adventure for . I have to say being an
44:01 guy. We're not very tech you know, so, uh,
44:06 this one anyway, I'm pleased about . Okay. Are there any questions
44:11 I go? Good question on evolved the class next semester. Excuse
-
+