© Distribution of this video is restricted by its owner
Transcript ×
Auto highlight
Font-size
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

-
+