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GEOL7324-Rock Physics - ThursdayOct7
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00:01 this conference will now be recorded. right, then, we left off
00:07 about the wily time average equation and roemer Hunting Gardner equation, you may
00:15 early on in the class, I a point of widely Gregory and Gardner
00:23 being L W. Gardner and Remer Gardner. Gardner being john gardeners,
00:30 relation as far as I know and neither related to jerry Gardner, famous
00:39 from University of Houston, who wrote Gardener and Gregory when he was at
00:46 Oil Research. So you can see difference between the widely equation which really
00:56 like it should be theoretically correct, it's not, it started out as
01:02 heuristic equation became an empirical equation because fit the data that Wiley had really
01:12 . And basically he said, the travel time one over the velocity is
01:16 slowness is equal to the volume fraction solid divided or times the travel time
01:25 the solid plus the volume fraction of times the travel time in the
01:31 So here, written in terms of velocities and the reverend Gardner equation is
01:40 in that it's written in terms of , not the slow nist and it's
01:48 to look close to the widely equation there's an explosion in here. So
01:54 one minus ferocity squared and to this , I have yet to find any
02:02 justification for this equation is purely There may be a theoretical justification because
02:11 find that it is going to be in many ways and certainly in ways
02:18 the widely time average equation defies physics Remeron Gardner equation seems to be better
02:27 . And so when I refer to reverend Gardner equation, I'm usually referring
02:31 this one. So velocity is equal one minus ferocity square times the velocity
02:38 the matrix plus ferocity times the velocity the fluid. They're nice things about
02:44 . For example, you can make , this will work for shear
02:49 If you set the velocity of fluid to zero, you can't do that
02:54 the time average equation. You can fluid substitute by replacing the velocity of
03:00 fluid here. And the answer is quantitatively correct, but its ballpark
03:09 And that won't work at all if try to do that with the widely
03:14 . So I happen to light this Now, it also tends to act
03:21 an upper bound as a practical upper . The void bound is way too
03:27 . There, there are no if mix solid material and ferocity there there's
03:34 rock that will come close to the bound unless you're very close to zero
03:40 . But no Rockwood appreciable ferocity will plot anywhere near the void bound.
03:47 highest things get is along the ray Gardner questions. So the reverend Gardner
03:54 won't be an envelope, It won't the absolute highest than anything gets but
04:00 most solidified rocks tend to flock along line somewhat above, somewhat below,
04:10 the widely equation is linear in transit , we'll see that the roemer and
04:16 equation is nonlinear in transit time. so it covers a wider range of
04:22 ease than the widely equation might. could usually go out to as high
04:29 37%. Now it's not common that have a highly liquified rock with 37%
04:36 . but you can get out that that far with this equation.
04:41 the as presented, the Raymond Gardner actually has three branches. It has
04:47 low porosity branch, the high porosity and the intermediate Brandt. This high
04:55 branch. It's written badly. There be parentheses here. I won't tell
05:02 who I stole this live from. you know, there should be parenthesis
05:06 around roe V P squared. And is roe V p squared equal
05:11 So I'll force you guys to What is roe V. P squared
05:17 equal to. I'm going to have be stubborn. You guys are going
05:32 have to think or use a pencil . Well, I mean uh numerically
05:43 what is it equal to? It units of for us. Well,
05:50 of stress because it's an elastic Which elastic module. This isn't do
06:05 math. What's V P squared V squared? Somebody tell me what bp
06:21 is is roe V P square. plane wave module us. Exactly
06:30 Bp squared is K plus four thirds of our OK plus four thirds
06:34 The plane wave modules. So BP is M over roe roe V P
06:41 is the plane wave modules. Very . So one over the plane wave
06:49 lists is equal to the ferocity divided what is this guy grow fluid beat
06:56 squared. What's that equal to? . Oak module lists of the
07:08 Exactly. And then one minus process divided by row zero. The zero
07:16 . This is the matrix. So would be the plane wave module us
07:23 the solid material. And we've actually this equation before we call this the
07:30 like equation, it's not the Royce . The Royce band would not be
07:36 flame waved module I it would be bulk module I only But in your
07:42 problem you you calculated the Royce average the plane wave modules, which comes
07:50 this because the plane wave module is equal to the bulk modules of the
07:55 . So, in fact, you've your homework, you've been using this
08:00 and you realize now from your homework it gives you a higher velocity than
08:06 Royce average. Does the Royce average you have any fluid, it fluid
08:13 a constituent. The Sheer Module Lists the Royce Averages zero. This
08:23 has some rigidity because it's inheriting some from K plus four thirds view of
08:30 matrix here. So this guy gives velocities that are slightly faster and so
08:40 probably more appropriate for loose sediments because in fact have some rigidity. If
08:49 could walk on them, they have rigidity. They're not truly purely in
08:57 . So anyway, that's what Raymond did by the way, this other
09:02 . This branch is not a theoretical . The wood equation is theoretical,
09:08 would like equation is in in the sense heuristic. But again it moral
09:17 there is, it sort of matches data so we'll go with it.
09:23 it's graduated to being empirical but really was probably just pulled out of the
09:29 . Somebody said so let me try . Okay, so let's look at
09:37 the roemer Hunt Gardner equation does here the high porosity branch is the dash
09:48 here. The low porosity branch is here. Now he gives it two
10:02 . He, the dash line here actually slightly different equation. Uh it's
10:11 this lower one. So that is purely empirical equation. And it's um
10:20 a little bit clumsy because you have use the density as well as the
10:25 . You need to know the matrix . That's an additional term. You
10:29 to know what presumably you knew it Already calculate the ferocity but maybe
10:35 but it's certainly a less satisfying And it wasn't clear to me what
10:43 the solid line here. And what the dash line? I suspect that
10:48 lower equation is the dash line because arrow seems to be pointed to
10:53 Uh huh. The black line is combined. So at high porosity
11:01 It's the high porosity branch. At porosity zits low porosity branch. And
11:07 between, in between 37 was Yeah, well, the way it's
11:18 , it looks like they started interpreting . Um maybe that's 37 Anyway,
11:25 between, they've interpolated between the two and they're comparing to the widely
11:35 So these two lines are the widely using different matrix velocity, 19,500 ft/s
11:45 a pretty good number for courts. sometimes 1900ft per second issues. That
11:54 gives you this line here, It you a slightly higher porosity at a
12:02 velocity. But sometimes people use a velocity of 18,000 ft/s. And that's
12:11 thing about the widely equation, which not satisfying because they'll use that matrix
12:19 even if there's no mineralogical justification for , you could be in a pure
12:25 sandstone And yet they're using a matrix of 18,000 ft/s. And you see
12:31 that does is it pulls the line a little bit and forces you more
12:37 the roemer and Gardner equation. Um know what I have a feeling is
12:46 other way because this goes through Now this is slower. Okay,
12:54 it's got to be using 18,000 Because fast one courts has zero porosity would
13:01 the lower transit time. So this would be more like 18,000.
13:06 it's moved the line down so it's in line with the roemer and Gardner
13:18 . And this shows that a little better. Here you have the true
13:24 matrix velocity here you have this uh modified matrix velocity which is non physical
13:34 some points will fall along that This is his would like equation compared
13:50 some measurements uh that were published some a publication of someone doing research for
13:57 Navy. The Navy was very interested underwater acoustics because of sonar. So
14:04 made velocity measurements on various thought sediments there's a bit of scatter here.
14:12 this would like equation more or less through the points. Again, it's
14:19 a true lower bound. Oh, now if you change the pathology or
14:31 have a mix of with Allah you can do that with the reverend
14:36 equation by taking the volume weighted average the velocities of the constituents. So
14:44 you're moving the line according to the . So if you're a dolomite,
14:49 is very fast, you have a intercept here, limestone in between
14:56 perhaps higher. And you could do substitution. So, uh here he's
15:03 a gas dance down there using a velocity of 2000 ft per second and
15:09 gives a not unreasonable result. Not correct, but not unreasonable. All
15:22 . Now we're going to do a of comparing of equations. You've seen
15:28 of these figures from me. So going to ask you to regenerate some
15:32 these So exercise 6.3 plot velocity versus and use the garden of sandstone
15:43 Remember that's a polynomial I gave to and it's slightly modified. So it
15:48 through the courts point the widely time equation. The wood like equation and
15:56 rain behind Gardner equation and use the velocity 1.5 kilometers per second of courts
16:03 of six kilometers per second. I on your test you calculated 5.93.
16:10 use six. It's convenient And go might as well go all the way
16:18 0 to 100% ferocity. All So just compare all those equations and
16:30 remember the gardener equation, The stand line is different from the overall Gardner
16:40 that you physicists know and love, some data from dr Hahn and so
16:54 plotted some of these lines and it's because he has the void average.
16:58 has the Royce average. You see Royce average makes a very good lower
17:03 , there was very little that disagrees it. And you have to wonder
17:07 you get a violation of the Royce . You have to wonder about maybe
17:13 they're measuring is wrong. Maybe the was wrong. Maybe the ferocity was
17:19 . Maybe the biometric volume fractions were , but you can see that no
17:26 at all come close to the void . Now here he is plotted the
17:32 porosity model, so he comes down be close to 40 and then he
17:40 avoid average of course with the module of this guy, this nearly unconsolidated
17:49 , by the way, you notice for the loose sediments here, you're
17:54 close to the Royce pounds is a high porosity, ease pretty loose sediments
18:01 slightly faster. And this is why would like equation pulls that line up
18:06 little bit to try to go through points I mentioned that the Raymond and
18:16 equation acts like an upper bound. it'll be interesting to compare the Raymond
18:22 equation to the critical ferocity model. think I asked you to do
18:28 One of your homework's let me I didn't ask you to do it
18:30 , but I think I will ask to do that. Uh here's the
18:36 time average equation. Some points plot it, but most points here are
18:45 below the widely time average equation. fact, the Gardener equation would probably
18:50 through this cloud, but there's a of variation along the cloud. So
18:57 can interpret this and let's forget about us because you add shale to Iraq
19:04 a given ferocity, the rock will slower if the process, you know
19:10 you have a clean sandstone and you a Shelly sandstone with exactly the same
19:16 and everything else being equal, the will tend to be slower because the
19:21 are more compressible and also they result flatter pores between the clays and between
19:27 clays and the sands. So, let's for the moment put aside composition
19:34 let's make believe that all of these are for pure court sand sounds,
19:43 could be true. I mean, could have pure quartz sand stones that
19:47 where these points plot. So let's assume that's the case. Then ask
19:57 what determines whether you're plotting near the bound or near this critical porosity model
20:06 bound what, you know, at given ferocity, I could be way
20:11 here or I could be way up , same ferocity. And one of
20:20 things that could explain that difference is degree of lip ification. You could
20:30 these rocks are highly liquefied. These are poorly liquefied. Another way you
20:38 explain that is by saying these rocks many more flat pores or maybe grain
20:47 acting like black pores, whereas these have primarily spherical for us.
20:56 So there are a couple of different we can explain this, but the
21:00 tend to go hand in hand, more liquefied, you are the fewer
21:08 these low aspect ratio pores that you have open, they'll get cemented
21:15 they'll get or if you're under they'll get closed. So these tend
21:21 be our shallow younger less live defied . These tend to be our
21:27 more liquefied rocks and deeper rocks. actually, as an attribute where you
21:34 in between these bounds is probably a attribute with geological meaning. Okay,
21:46 equations for the critical ferocity model where see that's the critical ferocity for sand
21:54 , we usually take it to be . But that could that could be
21:59 dependent and that could be sediment dependent well. But If you have no
22:06 information, 40% is a good number use for sand stones. So the
22:13 the critical porosity model works is you the module lists of the dry rock
22:23 this equation here. And use uh list of the care modules of the
22:30 rock using this equation here. And implies something about the V.
22:37 V. S ratio for the dry . So, for a homework
22:43 uh I'd ask you to think about . Remember the BP Ds ratio is
22:49 related to K overview because the density that when you take B P squared
22:55 the S squared, you're canceling density . So, K. A review
23:00 1 to 1 relationship with the P. P. S strata.
23:06 there's a pretty strong implication about ko you ratio for dry rocks using the
23:14 ferocity model. Now to calculate the porosity model for a brine saturated
23:23 this isn't going to help you because haven't gotten to fluid substitution later on
23:28 the course, if we have the modules of the dry rock and share
23:33 of the dry rock will be able calculate the velocity of the water saturated
23:38 , but you're not there yet. one thing you could do is just
23:43 this module is whatever it is in module is and just take avoid average
23:48 the two. So it's a volume average. Now, we also,
24:03 we were talking about ferocity mixed fine with coarse sediments in this case uh
24:13 went ahead and did the same thing measured the velocities. Remember we said
24:20 we mix a fine sediment with a sediment when we're somewhere in between,
24:28 we have, when we're all one all the other, we have high
24:34 . But when we're in between the grains of filling up the poor space
24:39 you lost ferocity, well, they something else happens. So that's what's
24:47 here. You can see that you clay two sand and it fills the
24:53 and you lose the ferocity. On other hand, you add sand
24:58 porous clay and you lose the They well they did that, but
25:05 also measured velocities and what they found the velocities. And I'm not,
25:09 don't remember if these are exactly the mixtures, but they found the velocities
25:18 maximum in between compression of velocity but share velocity shear velocity relatively insensitive.
25:29 anyway, that's something I'd like you chew on and try to come up
25:34 a hypothesis to explain why you would , hey hi, compression of velocity
25:43 not particularly high share modules or compression modules versus sheer modules. Yeah,
25:57 . Yes. Yeah. Now we have a way of directly assessing the
26:04 of micro cracks and that's by artificially Iraq. So, here's an example
26:12 they measured the velocity On a So this is a low porosity
26:19 1.7% porosity. And as they are axial pressure here. So this is
26:28 confining pressure, this is putting the in a piston and squeezing from both
26:39 . And as they squeeze the velocities . So presumably Iraq is fractured and
26:49 you're squeezing longitudinal e your closing the that are perpendicular to that direction.
27:00 , so if if I'm squeezing my horizontal fractures are going to close
27:08 presumably that's what's happening here. It's pretty big change in velocity. Now
27:13 is a dry rock. So the are having particularly large influence. But
27:20 closing up the fractures and the velocities starting to level off. They then
27:28 . Now, maybe it's the same . So, there could be some
27:33 says here or it's an equivalent but the velocities are going in the
27:39 direction. So we're not too worried history's is what they do is they
27:45 the sample. They make it glowing . He treated to 750°C. So you
27:55 some hell of another and then they it rapidly and that introduces fractures.
28:05 measure velocities on the fractured rock and see there is a bigger change.
28:11 ? Remember Math Co said that the of change is a function of the
28:18 . But to get this big wow, this is What a 40%
28:23 in velocity. That is a lot fracturing going on. Well to get
28:29 here. But the drop is almost right from the original sample to after
28:37 treating. So this thing is fractured hell. And you'll notice here at
28:44 a rapid increase. So, the fracture porosity, This is the
28:52 district difference between this velocity and the velocity here. That's an indication of
28:59 number of fractures. But when you a sharp rise, that's an indication
29:06 very flat fractures that are closing. . Now they never got back to
29:16 original velocity at a certain axial So why not? Why did they
29:22 get back to that velocity? That's you to answer. Mhm.
29:53 Nobody hypothesis doesn't have to be I don't care if your hypotheses are
30:00 or wrong. I just want to to see that you're generating hypotheses.
30:05 one of the things I hope you out of this course. Killing more
30:19 watering. Okay, so these are dry rocks and it's a gap
30:26 So I'm going to assume that there no water to the water.
30:32 I just want to get real. is a hypothesis. It's better than
30:43 like. That's better than silence guys you're getting two relatively warmer temperatures.
30:53 you starting to get like onset of metamorphic processes occurring minerals are rearranging and
31:00 like that? No, I don't so. But again, that's the
31:05 . Good. Keep in mind so heat it and then we call it
31:13 the measurements being made cool. So metamorphic processes would have had to have
31:19 irreversible then get frozen in. Oh . Mhm. Okay. So so
31:50 are these velocities increasing as I increase pressure? What's happening opposing the craft
32:00 cracks? Okay. So apparently I closed all the cracks. Why
32:10 Because it's still increasing? Because Because the velocity keeps increasing. So
32:18 saying if we had gone up to enough pressure we would have come back
32:23 that's possible. That's possible. But see it leveling kind of kind of
32:29 to this guy. I don't see trending that way where it's going to
32:33 back. It seems to me like is some irreversible deformation which I can't
32:45 . Not this way anyway. And give you a hint. Axial
32:52 Axial pressure. Mhm. So when apply axial pressure to a rock with
33:11 oriented fractures? Do I close all fractures? No, I'll close the
33:22 fractures are the ones perpendicular to the . But how about fractures parallel to
33:28 axis? I'll actually open those won't I? Yeah. So this
33:38 showing closure of horizontal and sub horizontal . But the axial pressure won't close
33:48 the fractures. Maybe if we'd applied pressure, it would have come closer
33:55 coming back. Now. Sometimes when generate these fractures, there are disparities
34:01 the fractures. You know what prosperity ? It's a roughness, right?
34:07 are Yeah, prominent. Their topographic sticking out from the fracture plane.
34:17 ? So, if I generate disparities then I have some slippage. So
34:23 fracture plane is not exactly, it's like south America and africa right things
34:30 moved such that they won't fit back . So, those disparities can prop
34:37 fraction fracture open. It's like having in the fracture. And so the
34:44 won't close all the way. that could be going on here
34:53 All right, guys, I want to generate hypotheses. So, here
34:59 the velocity measured on a granite while sitting on a desktop as a function
35:09 time. Is this sample like just the surface? Or is it from
35:26 a borehole? Let's say it's from surface. What exactly is the time
35:45 ? Uh You put The sample in apparatus, you measure its velocity time
35:52 . Then you measure its velocity an later measure it again two hours
35:56 20 hours later. Later when they to 70 hours later. So it's
36:01 three days later. Yeah. And noticed the velocity is decreasing. So
36:08 are ultrasonic measurements told at us like constant pressure. Yeah, pressure's just
36:21 no pressure. Okay. And if no pressure then the sample can't really
36:32 jacketed. Uh huh, ironic think the hypothesis that were proposed for the
36:48 case. One of those hypotheses actually to this case. Does does the
36:57 apply here? Yeah. Because the sample was what if it hadn't been
37:06 ? It had water in it and was drying as they were making the
37:16 . So saturation states important even in and metamorphic rocks. Okay, I
37:28 to admit this is a really hard . And I'm going to ask you
37:35 do it as a homework assignment and really going to have to put some
37:41 into this one. It's really complicated thing that's interesting here. Well,
37:50 comparing saturated and drawing measurements for p velocity and shear wave velocity. And
37:58 also doing it when the poor pressure the external pressure. So, what's
38:03 differential pressure here? When poor pressure confining pressure zero, zero. So
38:18 are zero differential pressure. But you the velocity is not constant. So
38:24 does that proof that proves effective pressure not equal to the differential pressure.
38:31 , keep that in mind. The measurement is made at a poor pressure
38:40 zero. How does it do Well, how do you make the
38:49 pressure is zero? If the rock saturated, that means it's not jacketed
38:55 you squeeze this thing as you increase pressure. It's like a sponge and
39:02 poor pressure doesn't build because the water not trapped in the sample. It's
39:07 time to a quick break and get . Actually, they drill a tube
39:13 the sample to measure the poor They have a a pressure gauge on
39:19 tube and they could assure themselves that poor pressure is zero. So saturated
39:28 zero pore pressure. We call this drains experiment. So the fluid,
39:35 of staying there and resisting the the fluid runs away. It it
39:43 want to deal with the pressure So it, quote, it gets
39:49 and never builds up any poor On the same sample measurements are made
40:00 and at high pressure. They're the at low pressure. There is a
40:09 for the p wave for the shear most of the time the dry measurement
40:18 faster than the saturated measurement, but very low pressure, the saturated measurement
40:26 faster than the dry measure. there are a lot of things going
40:33 here. So, I want you think about things like density change ferocity
40:45 the effect of the fluids in resisting compression. So come up with a
40:52 or this would be more of a . Right? Because you're going to
40:55 to explain many things so developed a to explain all of these data.
41:07 that's a tough one. This is to separate the men from the
41:11 I'm just warning. You don't say for the day before it's due.
41:15 huh. Mhm. Okay. Just the terminology straight. Uh skeleton pressure
41:32 external pressure, less internal pressure differential Equals confining pressure -4 pressure. So
41:47 the translation. So F. Bar is the differential pressure. So if
41:56 differential pressure is equal to the external , if the differential pressure is equal
42:02 the confining pressure, what is the pressure in that case guys, differential
42:25 equals confining pressure minus pore pressure, pressure equals confining pressure. What is
42:32 poor pressure you know? Yes. these measurements are at zero pore pressure
42:41 we've got increasing differential pressure. So is from Gardner, Gardner and
42:48 I think that's cut off from what can see. But the external pressure
42:54 then the differential pressure. I'm I take it back the external
43:01 The confining pressure external pressures from confining . F. Bar is differential pressure
43:11 lo and behold, what do you at different differential pressures when I have
43:21 same differential pressure. I have the velocity. So you could see here
43:27 this sample the differential pressure is equal the effective pressure because the velocities,
43:37 constant as long as the differential pressure constant. Everybody with me on that
43:47 . Yes. So here are two samples. Again, velocity versus confining
43:55 , same kind of measurements, Delta . Now is their differential pressure.
44:02 0 6000. And guess what? to being constant in this sample.
44:10 except that the very low pressures. . And you can say, you
44:18 , certainly not constant with differential but maybe you could say that's close
44:29 . So just keep that in The differential pressure is not the effective
44:35 close. So this is also from , Gardner and Gregory's paper. So
44:44 can read more about it in their and you're doing these exercises. And
44:49 , it's it's in your notes but just got clipped off and so he's
44:54 a slowness, stomach transit time here porosity and down deep he's obeying the
45:04 average equation. But with This matrix at 18,000 ft/s. But with that
45:13 of fudge, it's working these are velocities and ferocity is versus death.
45:24 shallow. You have a strong So these rocks are poorly lit defied
45:34 ified these widely time average equation Rocks more lift if I were getting closer
45:41 that upper bound, not quite but closer to it. Whereas here
45:47 deviate dramatically and there is the knee . Um This knee is probably and
45:56 saw the same knee when we looked porosity versus that. This is probably
46:02 depth at which you've finished rearranging grades deforming grade, you know uh deforming
46:15 structural framework, the arrangement deforming the of grains and compacted. All
46:24 so you have rearrangement of grains and of the grain. So you've reduced
46:31 of your porosity and now you're essentially we would call fully compacted. Not
46:39 lit ified yet. You saw the equation is below the practical upper bound
46:47 we're fully compacted. Mhm. Another of the same thing and this one
47:00 interesting. These are average velocities versus in Thousands of Wells, a couple
47:06 1000 miles I think they use and you see a knee, but if
47:12 take this ferocity at the very What was that? 5,
47:17 15, 20. Trying to remember the scale is on. Oh,
47:23 are just velocities. Okay, so here was 35%. And if you
47:32 put that sand pack under pressure and is what gas, when did remember
47:38 looked at that equation the other you just take the sand pack and
47:42 increase the pressure on it in the contacts deformed but you don't get
47:49 You know everything is very static. very nice and you apply more and
47:55 pressure to it. This is what . So you get a relatively linear
48:02 of velocity with death or calculated from pressure. She would have at those
48:10 . But what you see is a bigger velocity increase. Mm. So
48:16 you're fully compacted and then you reach point where you're more or less obeying
48:21 widely the time average equation, but quite your increasing velocity a little bit
48:28 than just the ferocity change. So have increasing degree of lift, ification
48:35 compared to the time average equation. as you're getting deeper and deeper,
48:39 approaching that fully lit ified why? of course, without rearrangement of
48:47 you can you can never get anywhere that higher velocity. All right
48:57 here's a complicated one to explain. , bear with me, it's a
49:04 story, but it's a beautiful So away from the mountains in the
49:16 in europe shale velocity was plotted versus , and limestone velocity was plotted versus
49:27 . So Came up with two linear . And then there in a location
49:37 has experienced a lot of uplift. it was very deeper. So it
49:47 high temperatures and pressures and was moved . Now it was 60% shell 40%
49:56 . So, with the limestone line the shale line, they're saying,
50:00 , we should have something Along this . C 40% of that and
50:08 I'm sorry, was 60% limestone, shale, I'm sorry, 60% of
50:13 , 40% of that. And so is the velocity versus death trend,
50:19 should have in the same age But what happens is you go to
50:29 particular, oh, you find these at very shallow deaths at these
50:42 The observed velocities were expected to be , but in fact they were
50:48 much higher as if they had been down to there. Yeah. So
50:57 seeing the pressure history have an So maybe these rocks were buried.
51:08 . That deep and uplifted and they have given us these philosophies. It
51:17 have been to that depth if the did not change as it was being
51:23 up. But in fact, these velocities up here as they get pulled
51:28 , they're going to be slowed somewhat the pressure is changing their stress
51:33 etcetera. So, in fact, huh These rocks may have actually been
51:40 . They may have been down here and they slowed up to there as
51:45 were uplifted. But anyway, gives estimate of the depth of burial,
51:56 the velocities are much higher than velocities have not experienced any uplift the burial
52:05 uplift. Yeah. Now, still at velocity versus depth trends turns out
52:17 the gulf of Mexico and a lot places *** delta, a lot of
52:22 rapidly deposit with high sedimentation rates basis high sedimentation rates. If you plot
52:32 shale velocities versus death, they tend follow a linear relationship. Well,
52:40 is transit time versus death. A relationship on a semi log scale if
52:54 normally pressure. So, this is a normal compaction trend. However,
53:04 huh. As you're getting deeper and as you follow this over compaction trend
53:12 you may encounter much slower rocks are shells. This works best in shells
53:19 they're more plastic and you see these best and shells. So from the
53:26 velocity you could detect where the poor are abnormally high. That the reason
53:32 shells are so much slower because they higher pore pressures pushes the grains
53:39 increases the porosity basically. So in previous case, the rocks were had
53:47 that were the same as deeper In this case we're talking about velocities
53:53 the same as shallow rocks. All . So this velocity here below 10,000
54:00 Is the same velocity that you would normally seen. And normally compacting shales
54:06 4000. The depth at which the pressure occurs often can be correlated to
54:18 transformations in your shells. So, example, in the gulf of
54:23 you have a transition from swelling shells have a lot of bound water absorbed
54:31 their crystal lattice. You have a transformation to ally expels the water.
54:38 this is another example of the But if you're an impermeable rocks,
54:44 water is leaving the play and it's to go someplace is going into the
54:51 space, but it can't escape, can't get out. So it increases
54:55 poor pressure, What does that It decreases the effect of pressure.
55:01 the effect of pressure here is similar the effect of pressure of 4000 ft
55:07 confining pressure is going to be were deeper, but are poor pressure
55:11 so much higher that the differential pressure much lower. And lots of examples
55:21 this, this is in velocity, it's a linear in velocity this
55:27 and this is a very empirical You kind of fit a trend by
55:31 to do this right. You really to be in in your cleanest shells
55:38 really should correct for composition and so . And compute the value that you
55:44 have for 100% shell and then look the deviation from that trend by the
55:52 , if you have a porous sandstone in communication with the surface, it
55:57 come back to normal pressure even if encased in geo pressure jail. If
56:04 the sand has a conduit to the the surface, you will have normal
56:10 in that sand. On the other , if that sand is not in
56:15 , so it's sealed off also that is going to have high pressure,
56:22 very dangerous because high pressure in a . If you drill through it,
56:27 sand is permissible, you could have blowout that high pressure cause damage and
56:36 can cause sparks as things were up each other. And if you've got
56:44 hydrocarbons in the system, which often , you often see hydrocarbons near the
56:50 of pressure, you can have an this result or if it's happening in
56:55 reservoir Iraq and people die as a . So it behooves us to be
57:05 to detect this in advance before the gotten there. You could clearly see
57:10 effects on well log. So here's sonic log. You see the slower
57:15 time. You also see it on conductivity log because the more poorest the
57:21 is, the more conductive it Um We could measure velocities using seismic
57:29 from the surfaces, their potential to in advance where the top of pressure
57:35 going to be. It's kind of a dead horse. Same thing in
57:43 basin. I do want to go some drilling scenarios with you suppose we
57:53 a seismically detecting these abnormally low Sorry, I have normally low
58:02 So here is our trend and our times are much higher. This is
58:07 seismic data. Then you can predict the departure from the normal compaction
58:15 You could predict the poor pressure required produce that difference and that tells you
58:23 mud way you need to have in to hold those fluids down in the
58:29 . And so you could have a mud way. Um So the black
58:36 here is the predicted poor pressure that would have and you need a mud
58:44 that is higher than that? Otherwise going to have a problem with
58:50 And this was in this. Well was the seismically predicted but way and
58:55 was the actual mud weight that the is used and it's not so
59:00 But there are a couple of points where they cross and that's not
59:06 They shouldn't cross. Those could be locations. However it won't be a
59:10 out if you don't have a permeable right there. Right. So if
59:16 if this is shale at that point would still be okay. Do they
59:25 do they usually plot the where the or where the formation would fracture?
59:31 beside that too? Yeah. And that gives you a narrow window.
59:36 you would have the the poor pressure and you would have the fracture pressure
59:43 and you need to keep your mud somewhere between those. So hopefully the
59:48 pressure gradient is up and here someplace the mud weight is between the poor
59:54 and the fracture pressure. The fracture is the pressure at which the formation
59:59 hydraulically fracture. And if you do while drilling you'll start pouring drilling fluid
60:06 those fractures. You'll have what's called circulation. And so that causes all
60:12 of problems with drilling. So you to you want to not fracture the
60:17 until you're ready to intentionally do You don't want to do it
60:23 So how did they estimate that? besides with an L. O.
60:26 . Test or F. I. . Test? Well the fracture pressure
60:34 be calculated from the elastic module. , there would be empirical relationships,
60:40 ? So you would predict from the , you would predict the elastic
60:46 I and then there are empirical relationships especially from Soissons ratio, you would
60:52 able to predict the fracture pressure. now we're we're venturing into the realm
60:58 drilling engineering and there's a slumber jay to do that. Uh which most
61:04 think doesn't really work too well. different pockets have their own equations to
61:11 and and really their empirical when you down to it. So anyway there
61:17 will be an equation from the velocities to predict the fracture pressure. So
61:28 just another example which I thought was interesting. The predicted four pressures were
61:33 than the mud weights. So you see the engineer is jacked up the
61:38 way up here. The geophysicists said you don't need to do that until
61:42 here. The engineers don't listen. then the chief said you need a
61:49 mud weight is greater than that. the trillion engineers didn't listen. Well
61:54 they were right. I thought this an interesting data set. And again
62:04 going to ask for a hypothesis we're seeing the anti Satrapi changed with
62:13 . So this is a case where p waves are velocities are measured parallel
62:20 betting or perpendicular to betting. So uh Well there are two ways to
62:28 it. You could drill plugs with orientations or you can put transducers with
62:35 orientations on the same sample. And be honest, I'm not sure how
62:40 did it in this case, probably same sample because the velocities came back
62:47 at high pressure that came back to equal. Uh So that's p wave
62:52 , shear wave velocity is a little different, shear wave velocity is a
62:58 of polarization parallel to betting or perpendicular . So that shear wave is polarized
63:09 a direction. So the trans verse of the shear wave could be parallel
63:16 betting or it could be perpendicular So this would have been the direction
63:22 propagation uh would have been which The direction of propagation. If we're
63:30 we're able to polarize parallel to betting perpendicular to betting which way there must
63:38 uh share wave be traveling. I'll you a hint it was travel.
63:45 the share way was traveling perpendicular to no matter how you polarize the shear
63:53 , you would be parallel to The the displacement of the shear wave
63:59 be parallel to betting. Do you that? I need to uh had
64:05 picture to this diagram. But so where horizontal it's horizontal propagation or
64:14 long vetting. But then you're polarised or parallel to the bedding. Uh
64:23 in both cases parallel tibetan is And that's kind of a rule of
64:32 , parallel to betting is more like columns, right? It's more like
64:36 boy average perpendicular tibetan is more like layers or crossing fractures. Right?
64:44 you're going to be slower. But we increase the pressure, the and
64:53 thought to be is decreasing. I a hypothesis to explain that.
65:18 What if I told you this was shell guests ferocity, ferocity is
65:30 Where instead of where you have grain green contact, which is uh showing
65:38 same behavior as how you said the , you're starting get rid of that
65:44 space or that softer material in Uh Yeah, but I'm gonna ask
65:50 to be more specific. Um you are closing up poor space.
65:57 pours, Are you closing? what's the definition of a shell?
66:11 You remember? Mhm mud rock? fissile. Exactly. And fissile means
66:21 a play d like structure? Probably of this play like structure is the
66:30 to part along bedding planes. so that's the definition of a
66:37 So the bedding planes act like a , their zone of weakness. And
66:43 long and flat. So they're low rations. Okay, so you can
66:51 this by closed by forcing the flames closed or just by you
66:59 even going more micro. And just at the pores between plates, between
67:05 clay platelets, between the phyllo silicate . And you're closing up those
67:14 right? Those are all are oriented a particular direction. Right? And
67:24 if you're propagating perpendicular to those bedding or your polarised perpendicular to those bedding
67:34 , or those flat pores between clay which are pretty well aligned. Remember
67:40 pressure, it's like a book, ? So we go perpendicular to
67:49 We're going to be slower, we parallel to those, we're going to
67:52 faster. But as we increase the , the distinction is decreasing because we're
67:59 up those fours. Everybody with You got that. That was a
68:07 one, yep. Okay, Okay, I really like this one
68:20 maybe I should have waited for the substitution section. But I mean we
68:27 talking about velocities. Oh, and we're going to look at velocities of
68:36 dry rock. So here's p wave , here's chua velocity and we had
68:45 . The velocity goes up, we salt water and the velocity goes up
68:52 . For the p wave, we kerosene, the velocity goes down for
68:57 share wave. And for brian, goes down even more. So for
69:08 homework assignment, I'm going to ask to explain the shear wave behavior.
69:19 , we're going to have to assume sheer modules is independent of the
69:24 Remember the rigidity of a liquid? . It doesn't matter what kind of
69:29 it is. And so I've given some numbers to play with here.
69:39 for your homework assignment, I want to explain why the big difference between
69:49 and salt water. Uh huh. is salt water so much slower in
70:00 ? Is the density different a difference to explain that? Or must something
70:05 be going on? Oh, Oh is Adam Mapco. And at a
70:27 we're going to assume the effective pressure the differential pressure. So just interpret
70:35 pressure is differential pressure. And we've different kinds of behavior comparing saturated and
70:42 as we increase the pressure in bedford , saturated rock stays high velocity.
70:51 dry rock approaches estimate chaotically. It like the water saturated results. That's
71:01 wave velocity, shear wave velocity. difference between the two. Something similar
71:08 happening in this granite and can say different in this dolomite, except the
71:21 rock is higher velocity than the dry for the shear wave velocity. All
71:30 , That's hard to understand. And this limestone, no difference between saturated
71:36 dry. So, we see different here. And I'm going to ask
71:42 to come up with hypotheses to explain . I'm not I can't mark you
71:48 , but it has to be a hypothesis. Right or wrong. It's
71:54 to try to explain the data. , if you haven't come up with
72:01 right answer, I'm not going to you wrong, I'm going to mark
72:06 wrong if you haven't come up with hypothesis. Oh that's right. Um
72:18 the difference between the low and the velocity is an indication of how many
72:24 you have and the rate of change long it takes to get to that
72:33 . Uh The suit has to do the crack shape, very flat,
72:38 will close very early at low pressure bring you near the high velocity whereas
72:45 higher the aspect ratio of the poorest longer it would take you to get
72:50 . Okay so I'm giving you part the answer for the difference in behavior
72:54 this guy and that guy. Oh quick could we get kind of a
73:03 oil shape where essentially if we had different poor shapes and stuff like that
73:09 kind of close one and then jump into another one. Yeah you
73:14 And we saw that with the gay was somewhat sig mortal. Okay.
73:19 . Yeah. Mhm. Okay so thought this one was kind of cool
73:29 there's some unusual behavior here so I'd you to explain it. Um And
73:38 Mapco is trying to point out here that if you're comparing different saturation
73:45 looking at impedance, remove some of ambiguity. Oh but there's some strange
73:54 here so spot it and come up a hypothesis to explain it. Okay
74:05 Any questions? Well then I'll stop
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