| 00:03 | So we're going to go back to exercise 6.8 and I'm in this |
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| 00:12 | I'm asking you to explain that the decreased the shear wave velocity decreased when |
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| 00:22 | added kerosene to the rock. And gonna say just get estimate the density |
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| 00:31 | Kerosene is .8 g per centimeter. our hypothesis is that adding fluid lowered |
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| 00:41 | velocity. So to test that we're going to calculate if we can |
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| 00:52 | the density in the rock, can lose the the density of the |
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| 00:57 | Can we reduce the velocity that So that's the problem. And since |
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| 01:05 | changes pretty consistent through most of I'm going to go up to the |
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| 01:12 | end here and I'm gonna start, need to know the the porosity of |
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| 01:21 | rock. So I'm gonna start with wave velocity of the brine, saturated |
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| 01:31 | , which gives me 11,600 ft per approximately. And then I'm going to |
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| 01:38 | a velocity porosity transform and to be , I don't recall which one I |
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| 01:44 | in this case, it might have been uh the gardener relation for sand |
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| 01:50 | um doesn't matter. This is just illustrate the point. And so I |
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| 01:57 | a density. So it is the relation. I go from velocity to |
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| 02:04 | and then assuming it's pure courts, go from density to porosity. So |
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| 02:13 | that's pretty straightforward. Now what I to know to calculate the change of |
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| 02:21 | wave velocity. I need to know sheer modular and I need to know |
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| 02:26 | density dry. And I need to to the density dry to the density |
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| 02:36 | it's fully carriage and saturated. And do that I'm gonna use the mass |
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| 02:43 | equation but I need the sheer modulates where do I get that from? |
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| 02:48 | it's I have V. S. the brine saturated rock here I have |
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| 02:57 | I could just say roe V. squared. So I have density. |
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| 03:02 | brine saturated rock, I have roe . S squared. And that would |
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| 03:08 | me you know of course I have convert BS2 km/s. And so I |
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| 03:16 | V. S. Which was 6400 30 to 81 ft per second. |
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| 03:22 | gives me B. S. And per second. I multiply square that |
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| 03:28 | by density. That gives me the modulates. Excuse me then, given |
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| 03:36 | ferocity I could calculate the density of dry rock is just one minus ferocity |
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| 03:43 | the grain density. Which if we're courts it's 2.65. And then I |
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| 03:50 | calculate the density uh saturated with Karajan the mass balance equation. Okay, |
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| 04:01 | now I've got the density of the in saturated rock. I've got the |
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| 04:06 | module asse. So I could take module is divided by density, take |
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| 04:12 | square root And calculate the shear wave of the dry rock. I get |
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| 04:18 | 40 for and that's compared to the which was about 60 800. Um |
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| 04:28 | I'm sorry for the kerosene, saturated was 64 55 the measurement was |
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| 04:35 | So we're pretty close. Okay, that's the process. I walked you |
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| 04:40 | it fast, but now I'm gonna you reproduce that process. But instead |
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| 04:49 | using the gardener relationship here, I to get this a little bit |
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| 04:54 | So I'm gonna guess, say the is 15%. So with a 15% |
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| 05:02 | . Then go through this process uh and walk me through it as |
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| 05:10 | doing it. Show me the steps taking. So uh since you have |
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| 05:16 | on your ipad then I'll allow you share your spreadsheet as we walked through |
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| 05:22 | process. So go ahead and do . I'm gonna stop sharing. |
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| 05:35 | We talked about these and here we're at the effects of poor fluids on |
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| 05:45 | p wave velocity and these are in rocks as a function of pressure. |
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| 05:52 | here we have a low porosity And for p wave velocity fully saturated |
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| 06:00 | the highest oil has a smaller bulk , so its velocity is lower, |
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| 06:07 | air has the lowest bulk modulates so velocity is lower. And you notice |
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| 06:14 | we increase pressure uh the bulk, sorry, this is bulk module |
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| 06:19 | Okay, so anyway, you get . So the bulk module asses increasing |
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| 06:26 | pressure as we're compacting the rock, it stronger. But notice it never |
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| 06:32 | off. That suggests that we have wide range of aspect ratios here in |
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| 06:39 | font and blow sandstone. You notice was a precipitous increase in first and |
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| 06:45 | it levels off. So here we cracks that are closing here we have |
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| 06:52 | variety of shaped pores and as we pressure we still haven't closed all of |
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| 07:00 | . So that kind of explains the in these two behaviors. Now. |
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| 07:06 | the other hand, when I go velocity I find that oil and dry |
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| 07:12 | pretty similar, right? Whereas the modulates was different um when I go |
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| 07:19 | velocity, we're pretty much the So I need a hypothesis to explain |
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| 07:27 | in this case. I mean pressure's . So I feel like the answer |
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| 07:53 | compaction but I'm not. No. Well the question is if there's such |
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| 07:59 | big difference in dry modular from why are they why is the velocity |
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| 08:08 | the same? Mm. I don't the answer but I need a hypothesized |
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| 08:17 | . Doesn't have to be right. worries there. Um Let's see. |
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| 08:27 | , their clothes because so many questions unleash. So think about the equation |
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| 08:43 | p wave velocity and think about the that could be changing could be different |
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| 08:50 | oil and air. We know that has a higher bulk modules. So |
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| 08:58 | suggests the velocity should be higher than air case. But something else is |
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| 09:05 | as well that's canceling out that bulk effect. What else could be |
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| 09:11 | There are only two other things that be changing. It could The equation |
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| 09:18 | p wave velocity, square root of plus four thirds mu over rho if |
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| 09:24 | is increasing from the from the dry , what else could be decreasing to |
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| 09:35 | that effect? The densities? the density could be increasing enough to |
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| 09:43 | that effect. Right. So maybe density and the bulk modules are increasing |
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| 09:49 | the same amount, thereby canceling the . The other thing that could be |
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| 09:57 | is the sheer modulates of the rock be different when oil saturated versus |
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| 10:05 | But that is a little bit Right, so the suggestion here is |
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| 10:10 | the density effect is canceling out the asse effect with me there. |
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| 10:19 | But then when we go to p impedance, oil is again higher impedance |
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| 10:24 | dry. Uh even though their velocities the same. So how can the |
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| 10:32 | be the same? But the impedance greater for oil versus dry. How |
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| 10:37 | that possible? Um Well, because , doesn't oil hmm. Well, |
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| 10:55 | a big higher resistance, doesn't Well, I think you mean viscosity |
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| 11:01 | also. Well, yeah, but about the equation for impedance, what |
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| 11:07 | give you the impedance, What is equal to? Um It's able to |
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| 11:24 | is it? It's a I can't right now but I know, do |
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| 11:39 | remember the equation for reflection coefficient Right, this second. Alright, |
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| 11:54 | impedance is velocity times density. That's you may have seen the reflection coefficient |
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| 12:02 | , wrote two V two minus row V one. I mean no one |
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| 12:05 | one over rho two V two plus one V. One. It's the |
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| 12:11 | in impedance divided by the sum of impedance is is the reflection coefficient |
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| 12:17 | So here p wave impedance is velocity density. Well oil and dry have |
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| 12:26 | velocity and yet oil has higher What does that mean about the oil |
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| 12:33 | sand versus the air saturated sand? have the same velocity. What must |
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| 12:39 | different for the impedance for the oil to be higher? Yeah. And |
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| 12:46 | already said that that's probably why they the same velocity because oil is more |
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| 12:52 | than air. Okay. Um Yeah it this is a strange situation on |
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| 13:01 | right because in this case water is dense than oil but its velocity is |
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| 13:18 | . Here we have the dry the velocity is higher than the water |
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| 13:25 | rock which is higher than the oil rock. Any ideas here? Any |
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| 13:33 | to explain this? So, is possible that oil lower the share modules |
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| 13:51 | could be happening? This is from coz corn oats. Uh course |
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| 14:00 | And he says the density effect explains but I'm not sure it does. |
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| 14:07 | mean what he's saying is if the increases more than the module asse you |
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| 14:12 | actually decrease the velocity and that might if you had very circular pores. |
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| 14:21 | circular pores are not very compressible and porosity is pretty high. So uh |
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| 14:30 | you see, so he's suggesting that change in density is more than the |
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| 14:36 | in the modular. I have a time with that. I think it |
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| 14:41 | has to do with um uh somehow the sheer modulates of the rock because |
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| 14:49 | systematics in this case aren't quite Water is more dense than oil and |
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| 14:56 | oil is lower velocity than water. ? So you see in bulk module |
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| 15:03 | water, oil dry. The density for water must be bigger than the |
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| 15:12 | effect for oil. So it's a a little bit odd what's happening |
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| 15:18 | But of course, you know, they have more information. Oh by |
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| 15:23 | way, there was the answer, is density times velocity. It was |
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| 15:28 | there. Um So um anyway, rare for the density effect to dominate |
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| 15:36 | p wave velocity, but the density usually dominates on shear wave velocity. |
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| 15:48 | , so remember I said yesterday that affects the fluids and not so much |
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| 15:57 | solid material. Well especially the it could affect the organic matter, |
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| 16:03 | not so much the minerals. So we have a rock and measuring the |
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| 16:12 | as pressure is changing and his temperature changing. I'm sorry, his temperature |
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| 16:21 | changing this way. So the velocity decreasing with increasing temperature and yet the |
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| 16:30 | is decreasing with increasing pressure. So don't tell you what pressure this |
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| 16:38 | So could you tell me, can guess is this effective pressure? Is |
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| 16:42 | confining pressure? Is it poor What kind of pressure is this that |
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| 16:49 | I increase it I reduce the velocity pressure. Well if I increase confining |
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| 16:58 | then the velocity goes up right? I hold poor pressure constant and I |
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| 17:04 | the confining pressure velocity goes up because differential pressure goes up. So which |
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| 17:13 | would I have to increase to reduce differential pressure? Yes. So they |
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| 17:22 | tell you what kind of pressure this . But this is the poor |
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| 17:26 | And so they increase the poor The velocities go down. Now if |
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| 17:32 | velocities go down as I increase which bulk module asses changing? Is |
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| 17:41 | the bulk modulates of the solid grains the bulk modulates of the fluid? |
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| 17:47 | it's got to be the bulk modulates the fluid as the temperature goes |
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| 17:52 | the fluid wants to expand. So going to uh if it expands then |
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| 18:00 | becomes more compressible. Right? The are further apart from each other. |
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| 18:06 | it's easier to compress them. So I increase the temperature, the bulk |
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| 18:11 | of the fluid is dropping. So typically what you find is that as |
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| 18:21 | increases this is a water saturated rock the velocity decreases. So here we |
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| 18:29 | higher differential pressure here we have lower pressure and even lower differential pressure. |
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| 18:38 | the velocities decrease at the smaller differential . And as temperature increases, the |
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| 18:47 | decreases shear wave velocity. On the hand, here, the velocities are |
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| 18:56 | constant. Now he's fit a line , but I would argue that this |
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| 19:02 | is dominated by that point and I say that within the experimental error, |
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| 19:10 | am willing to say that that is . And I'm also willing to say |
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| 19:15 | that is relatively constant. So the here is that as I increase the |
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| 19:24 | , I'm not supposed to if I'm changing the fluid module, asse, |
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| 19:28 | not supposed to change the shear wave . But as the fluid expands at |
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| 19:34 | temperature, the density, it becomes dense so the density goes down. |
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| 19:41 | actually the velocity should increase with So, I'm not sure I accept |
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| 19:49 | results where he shows velocity decreasing with temperature. There may be other things |
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| 19:57 | on as the fluid expands, maybe up cracks that were otherwise closed, |
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| 20:05 | the velocity to decrease Anyway, I see any compelling argument or data to |
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| 20:13 | me that the shear wave velocities are here with increasing temperature. Now, |
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| 20:24 | course, as I get to very temperature, I can freeze the water |
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| 20:30 | the pore space. And when that the water becomes solid, it develops |
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| 20:36 | . And so the p wave velocity way up, shear wave velocity goes |
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| 20:45 | even more. This is a huge on the north slope of Alaska because |
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| 20:52 | the near surface you have permafrost that frozen all year round. But in |
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| 21:01 | summer it starts to melt. So could have dramatic changes in velocity and |
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| 21:10 | , you know, as I'm moving in someone case, I may be |
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| 21:15 | frozen in another case where the sun to be concentrated, I may be |
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| 21:21 | melted. And so there are dramatic variations. Also when that permit for |
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| 21:28 | starts to melt any heavy equipment on would sink into it. And so |
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| 21:36 | seismic acquisition season in uh, on north slope of Alaska is only |
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| 21:46 | when everything is frozen, the temperatures to be close enough to be |
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| 21:51 | This way, the equipment can move over the ground and you don't have |
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| 21:59 | variations. You don't have big changes near surface velocities. Okay, |
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| 22:11 | um, later on in the we'll talk about how we calculate the |
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| 22:18 | of fluids on the rock. What did today was just considering the density |
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| 22:24 | , but we want to be able calculate how the bulk modulates of the |
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| 22:29 | changes with the fluid. So, , hill fred Hiltermann, uh paints |
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| 22:37 | or draws rocks looking more like swiss , right with big holes, These |
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| 22:43 | the pore spaces. So you have material around the holes. This is |
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| 22:48 | little bit unrealistic rock but it it the different materials that will be |
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| 22:58 | So we have the pores and that's to say porosity there. So we |
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| 23:04 | the porosity of the rock. That's be important. Now as I try |
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| 23:09 | compress this rock, so I'm going a larger cube to a smaller |
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| 23:14 | Remember if it's volumetric compression? The stays the same. So I have |
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| 23:20 | bulk modulation of the whole rock but also have the bulk modular of the |
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| 23:28 | . So I have the bulk modulates the fluid. And we saw how |
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| 23:32 | can affect the velocity of the meaning it affects the bulk modules of |
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| 23:37 | rock. We also have the bulk of the solid material. Now what |
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| 23:45 | going to compress as I'm compressing the , it's going to compress the solid |
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| 23:50 | , it's going to compress the fluid it's gonna compress the entire rock |
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| 23:56 | Right? That rock frame could be strong or it could be very compressible |
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| 24:03 | on the shape of the pores So I need to know the bulk |
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| 24:08 | of the rock frame not with with help from the fluid. So they |
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| 24:13 | call that K. Dry. Uh the effect of the fluid out. |
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| 24:20 | We'll talk about if that really is dry or it's something else. But |
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| 24:26 | just terminology. We call it the module asse of the dry frame or |
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| 24:31 | dry skeleton without the fluids in we have the bulk modulates of the |
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| 24:38 | and we have the bulk modulates of solid material. So the frame will |
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| 24:43 | , the fluid will compress and the material will compress. So to calculate |
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| 24:49 | bulk modulates of the saturated rock, need to know all of those bulk |
|
| 24:54 | I and uh we'll go through the later in the class. But I |
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| 25:05 | then calculate if I have those if I know the ferocity, I |
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| 25:09 | the bulk modules of the frame, know the bulk modulates of the fluid |
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| 25:15 | . And I know the bulk module of the solid material. And of |
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| 25:20 | I I have to know the densities all of these. Then I could |
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| 25:25 | the change in velocity as I changed water saturation. So here I'm 100% |
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| 25:35 | here, I'm 100% water. As add gas to fully water, saturated |
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| 25:43 | , the bulk modulates of the rock dramatically and the density increases a little |
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| 25:49 | , so the shear wave velocity goes because of the density increase. But |
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| 25:55 | p wave velocity goes down because of bulk module is decrease. So a |
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| 26:01 | bit of gas goes a long way drops, the velocity a great |
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| 26:05 | And this is according to Woods equation the bulk modulates of the fluid drops |
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| 26:13 | . Remember the wood equation, or Royce bound is dominated by the smallest |
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| 26:20 | . And bulk modulates of gas is small, so it will dominate. |
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| 26:27 | after I've added just a little bit gas, I've already dropped the bulk |
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| 26:32 | of the fluid so much, it change anymore. And then the only |
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| 26:37 | that happens is the density changes and the velocity rebounds a little bit. |
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| 26:44 | , if this is a very porous with very spherical pores, those pores |
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| 26:49 | so strong that the drop in velocity to the gas may not be much |
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| 26:55 | the density effect may be so large in fact theoretically the dry rock can |
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| 27:02 | a higher velocity than the water saturated . Okay, so we'll go through |
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| 27:12 | equations later in the course. But now we'll look at a simple empirical |
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| 27:19 | between the velocity of the brine sand the velocity of the gas sand. |
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| 27:24 | that's the solid line here. The line is if they were equal, |
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| 27:29 | solid line is showing that when I low velocity rocks, the rock frames |
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| 27:38 | very compressible. So changing the fluid a big effect. I have a |
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| 27:45 | difference in velocity. The gas sand is much lower than the brine sand |
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| 27:51 | . If our if our on the line here, they would be equal |
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| 27:55 | , the gas and velocity is much than the brine sand velocity. So |
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| 28:01 | bride same velocity is a good indication how big the gas effect is gonna |
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| 28:08 | . And so here but below, know, 12,000 or so feet per |
|
| 28:12 | , the gas effect is relatively But as I increase my p wave |
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| 28:17 | , the gas effect gets smaller until get extremely high here. And this |
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| 28:23 | be explained by the porosity czar very . But the, you know, |
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| 28:27 | velocities are high as a result, you have a lot of micro |
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| 28:32 | So the fluid effect is large because microfractures are very compressible, but the |
|
| 28:40 | change in velocity is even smaller. ? You know, because if I'm |
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| 28:46 | at the percent change from brian to , these velocities are high. So |
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| 28:51 | difference is a small percentage whereas here same difference would be a much larger |
|
| 28:58 | of the velocity. So the moral the story is young, shallow porous |
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| 29:05 | that have low p wave velocities then a big gas effect and hard rocks |
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| 29:11 | a small gas effect. So this us to the issue of direct hydrocarbon |
|
| 29:25 | . If gas drops the velocities, will also drop the impedance. Right |
|
| 29:32 | will drop the density and will drop velocity of the rock. So if |
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| 29:37 | have an impedance of shell which is square here, relative to the |
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| 29:44 | If the brine filled rock is low relative to the shell maybe because its |
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| 29:50 | porous or maybe because the shell is cemented, um I'll have a negative |
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| 29:58 | coefficient there. And if I add to the brine, or if I |
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| 30:03 | brine with gas, I lower the more because I lower the velocity, |
|
| 30:09 | lower the density. So here I a more negative reflection coefficient. |
|
| 30:15 | So I have a negative amplitude for , but I have a more negative |
|
| 30:21 | for gas, that's called a bright . And this only happens when you |
|
| 30:28 | a low impedance reservoir when the the field rock and the gas field rock |
|
| 30:34 | low impedance relative to the shell. the other hand, if the p |
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| 30:41 | and penis of the brine filled rock higher than the shell, you can |
|
| 30:48 | you lower the impedance than you're going a strong positive amplitude for the brian |
|
| 30:54 | to a weaker positive amplitude, both high impedance relative to the shell. |
|
| 31:00 | the gas and reduces the reflection that gives you a dim spot. |
|
| 31:07 | , if that change in uh in is so large or if the sand |
|
| 31:14 | only slightly greater than the shell in for when it's brian saturated, that |
|
| 31:20 | in impedance when you get add gas flip the polarity. So you could |
|
| 31:26 | from a positive reflection coefficient to a one and that's called a polarity |
|
| 31:34 | That polarity reversal can also be a spot. If the effect is real |
|
| 31:39 | . If the gas sand is out , that would give you a bright |
|
| 31:43 | . Or it could be a dim , if the result is near zero |
|
| 31:48 | you add gas. So we like have an expectation of what kind of |
|
| 31:58 | anomalies to expect. And so this where rock physics comes in. So |
|
| 32:04 | go to our well logs and we'll usually find shells and brian sands and |
|
| 32:11 | plot their average velocity versus depths. and density. So the density tends |
|
| 32:17 | increase with depth, the velocity tends increase with depth. If the sands |
|
| 32:23 | lower velocity than the shells and lower , then there will be low impedance |
|
| 32:31 | we'll get bright spots because the gas are even lower velocity and lower |
|
| 32:39 | So usually the brine sand velocities are from the logs and then we do |
|
| 32:46 | substitution. We use gas men's equations predict the change in velocity. So |
|
| 32:55 | though we don't have gas sands at depth, we could calculate what their |
|
| 32:59 | would be. Now things are not this well behaved. Usually they're not |
|
| 33:08 | you don't you're dealing with different stands different depths. So they may have |
|
| 33:13 | a different porosity from the time of . So think of these as average |
|
| 33:21 | velocity densities and velocities versus depth. so what you could do is calculate |
|
| 33:27 | reflection coefficient and you hear here in white is the brian sand reflection |
|
| 33:35 | The black is the gas and reflection . These are negative numbers and uh |
|
| 33:43 | gas sand is more negative than the sand brian sand. So in this |
|
| 33:47 | these are all bright spots. But that the difference between the gas amplitude |
|
| 33:55 | the brine amplitude decreases with depth on average, that difference decreases with depth |
|
| 34:04 | the fluid effect is getting smaller with . As we as the brine sand |
|
| 34:10 | gets higher, the fluid effect, change in velocity gets smaller and as |
|
| 34:18 | porosity is decrease, the change in gets smaller. Okay, so here |
|
| 34:28 | an example of gulf coast uh velocities depth for a brine sand for an |
|
| 34:40 | sand with fluid substitution with a gas with fluid substitution and with a |
|
| 34:47 | So if we ignore the density effect the moment and assume that everything is |
|
| 34:55 | by velocity. Then here the brine is high impedance. The gas sand |
|
| 35:01 | low impedance. So here shallow you a clarity reversal. Uh for |
|
| 35:10 | it would be a dim spot. see that? Okay, here in |
|
| 35:15 | range here everything is negative. So are all bright spots by the |
|
| 35:22 | that polarity reversal is bright as well it's the gas sand is more negative |
|
| 35:29 | the brian sand is positive. then we get this crossover where the |
|
| 35:35 | sand and this is pretty typical as get deeper, the brine sand becomes |
|
| 35:41 | than the shell, the gas sand softer than the shell, lower |
|
| 35:47 | So we have a polarity reversal at point the gas sand equals the shell |
|
| 35:55 | . And again, ignoring the density for the moment. That would suggest |
|
| 36:00 | dim spot in this case. So can see that as a function of |
|
| 36:07 | , we could alternate between bright dim spots, polarity reversals, et |
|
| 36:15 | . Down down deep here it looks we're headed towards the polarity reversal |
|
| 36:20 | but keep in mind, I've ignored density effect. Just just to illustrate |
|
| 36:25 | happening. Um you really have to into account the density to determine. |
|
| 36:35 | know, you need this plot of rather than velocity in order to determine |
|
| 36:40 | you're going to have bright spots, spots or polarity reversals. Now, |
|
| 36:47 | , these curves are averages based on of measurements with fluid substitution. |
|
| 36:54 | So these are just these are not to tell you what a particular individual |
|
| 37:01 | is going to do because there are around the average value. So, |
|
| 37:09 | an example of hissed a grams of sand velocities. Shell shell velocities and |
|
| 37:18 | sand velocities here, the brian sands slightly on the average faster than the |
|
| 37:24 | , but not always a particular This shell is going to be faster |
|
| 37:30 | that. That brian sand. So even though the average might be |
|
| 37:35 | little higher for brian sand, uh not necessarily the case. And here |
|
| 37:41 | the gas sands. And look, have some gas sands that are higher |
|
| 37:45 | than the shells. Some are lower the shells. So you can't judge |
|
| 37:51 | gonna happen just by the mode or mean of these distributions, a particular |
|
| 37:59 | maybe behave differently from the average we've converted the velocities and also done |
|
| 38:08 | same thing for the densities and computed for reflection coefficients. And in this |
|
| 38:17 | uh this is at a particular The brian sand tends to have positive |
|
| 38:24 | coefficients or near zero, and the sands tend to have negative reflection |
|
| 38:31 | but you can see there's overlap on distribution. So a particular gas sand |
|
| 38:37 | have a higher velocity than or it have a higher reflection coefficient than a |
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| 38:45 | brine sand. So this this is fred Hiltermann and he's plotting velocity for |
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| 38:56 | velocity for shale versus death. So getting his instagrams versus death. These |
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| 39:02 | from well, logs, okay, going back to the average values. |
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| 39:15 | we have an average reflection coefficient for sands here and an average reflection coefficient |
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| 39:23 | gas sands. So here where the Reflection coefficient for wet sands is zero |
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| 39:35 | it, the wet sands are So gas sands are going to be |
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| 39:41 | negative. So you're gonna have bright here, when the brine sand goes |
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| 39:48 | , the gas sand can still be . So you'll have polarity reversal. |
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| 39:52 | this is the first crossover. We from bright spots to polarity reversals. |
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| 40:00 | when the gas and becomes higher impedance the shell at that point we switch |
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| 40:06 | dim spots. So this is a tendency, you tend to get bright |
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| 40:11 | shallow polarity reversals, intermediate and dim deep, but as I said, |
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| 40:20 | that can vary all over the This is just a general tendency. |
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| 40:25 | seen bright spots very deep and I've dim spots very shallow and I've seen |
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| 40:32 | bounced back and forth from santa sand , you know, 1000 ft interval |
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| 40:37 | example, you could go from one the other and back pretty easily. |
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| 40:47 | if we uh take into account rouse and we calculate whether where this cross |
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| 40:57 | cross over depth is as a function age here. So this is a |
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| 41:03 | , this is depth, this is crossover where we have zero reflection coefficient |
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| 41:09 | the brine sands. Uh If we're that trend, we have positive reflection |
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| 41:17 | . If we're below that trend we negative reflection coefficients. So that the |
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| 41:23 | way as as you get deeper, tend to get dim spots as you |
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| 41:28 | older, you tend to get dim so very young tend to have negative |
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| 41:34 | as we get older, we would to have positive reflections. Okay, |
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| 41:43 | it for this section. So uh stop recording uh any questions before I |
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| 42:00 | . So in the next section is . P. B s ratios and |
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| 42:05 | gonna go back to our old friend ratio, which has uh Ellen said |
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| 42:14 | is uh squash divided by was it divided by squash. Um Trying to |
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| 42:25 | the terminology we used but it's the change in width divided by the fractional |
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| 42:33 | in length. So squish over Yeah squish over squash. Yeah that |
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| 42:42 | that should be standard terminology I think good. So um it's the transverse |
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| 42:50 | divided by the longitudinal strain. And as we propagate waves through Iraq we're |
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| 43:00 | and squashing. Right? So there a direct relationship between the velocities and |
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| 43:07 | poison's ratio. And this is the . So it goes to the |
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| 43:14 | P. V. S. Ratio means it's independent of the density. |
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| 43:19 | it has to do with the ratio the module I it's really K over |
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| 43:23 | plus four thirds is V. B. S squared. So there's |
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| 43:28 | direct relationship between prisons ratio and P. B. S. So |
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| 43:35 | is the person's ratio When V. . V. S. Is equal |
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| 43:38 | the square root of two? Right square 22 squared is 22 minus |
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| 43:50 | gives us zero. So and that's the lower practical limit. Remember we |
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| 43:58 | that theoretically poison's ratio could be as as minus one. So what the |
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| 44:07 | ratio would correspond to a song's ratio -1 one. No math I thought |
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| 44:20 | did hold on Square root of 4 exactly Which is 1.16. So that's |
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| 45:21 | theoretically lowest V. P. S ratio. We could have |
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| 45:29 | What's the highest vp uh What's the persons ratio? We could have |
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| 45:38 | And what is the VPs associated with ? I've been a little trouble with |
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| 46:17 | math, aren't you? We have p B s squared minus one equals |
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| 46:24 | P B s squared minus two. . Mhm. Do you see |
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| 46:32 | So what number would that work Where would you where would you have |
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| 46:43 | P. B. S squared minus equals V P B s squared minus |
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| 46:54 | . I mean If the PBS is then -1 or -2 wouldn't matter. |
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| 47:02 | . So you'd have infinity squared equals squared. So really cousins ratio is |
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| 47:12 | as V. P. B. approaches infinity. Remember for a fluid |
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| 47:18 | wave velocity is zero. So that's infinite V. P. B. |
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| 47:27 | . And poisons ratio .5 corresponds to fluid. So when we make the |
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| 47:46 | measurement, we have a cylinder. has a original length and original |
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| 47:54 | And we now put a uni axial on it. We don't constrain it |
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| 48:01 | . So it's free to squish as squash it. So uh the change |
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| 48:10 | |
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