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GEOL7324 Rock Physics - Day3 10-28-2022
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00:00 beef. Thank you. So I don't do this with my classes but
00:08 week I have attended a presentation and given the recording and it is such
00:16 good introduction to the rock mechanics aspects rock physics and really a great overview
00:25 BP. And so it's long but very clear and it's uh you
00:33 starts from the very basics and so thought we would listen to the whole
00:39 . I mean it's a much better than I can do. So I'm
00:45 play this if at any time you me to stop it to ask a
00:50 , don't hesitate to do so. I'm gonna start it now. Let's
00:55 you can hear this. Okay. it all works. She's our biomechanics
01:00 within BP. She's been extremely instrumental helping out with the poor pressure fracture
01:08 work for drilling wells especially RCC US and but she has a multitude of
01:16 ranging from P. P. G. To uh wellbore stability and
01:23 risks and also uh fault reactivation and she's just all around great person to
01:30 on the team. She's she's been a source of joy and happiness and
01:36 a wonderful uh levity to the So happy to have Ellen here.
01:42 there's anything I missed on, maybe sure I didn't do justice. So
01:48 please expand on that. No Let me just get things shared and
01:53 I will go ahead and introduce thank you Cory. Um yeah as
01:59 said, my name is Alan I'm a mechanic specialist here at
02:03 Um and I've been, I've wow, I've been with BP for
02:08 years now um and really done for and game mechanics the entire time of
02:13 career here, including after a PhD Geo mechanics out at Stanford University with
02:19 Zoback. Um so at this point say geo mechanics is in my
02:24 Um I've been pretty involved from the with the C. C.
02:28 S. Stuff. This last integration BP having a lot of fun.
02:33 a it's a really interesting topic from Geo mechanics perspective, so excited to
02:39 of share some of my thoughts on . Give a little bit of geo
02:42 background for those of you who maybe heard of it, but don't have
02:46 deep understanding of it and then talk how it applies in a C.
02:50 . U. S. Space. So yeah, that's basically it.
02:56 don't know how many people we I don't know how you guys handle
02:59 if people do have ones. Um I could have somebody keeping an eye
03:03 that, just in case I missed , if somebody does have a question
03:06 be great, okay and they may they may show up in the chat
03:15 then we can go through all them at the end, so not to
03:18 your talk. Okay. Perfect. if something is unclear as I'm going
03:23 , feel free to feel free to that some of this, once you
03:27 a technical piece, it kind of you going forward. So, so
03:33 a quick introduction, if we think for pressure and Geo mechanics in in
03:40 space of C C U S. know, you guys have all probably
03:43 a lot about this but you there are three real keys to a
03:47 Ceo to storage project. Right? that starts with containment Capacity of your
03:54 unit and the ability to mark that unit and where the CO2 is actually
03:59 to at the end of the day pressure and Geo mechanics are absolutely integral
04:04 all three of these. And unlike lot of more traditional oil and gas
04:11 can access the potential to be a showstopper. So in that for that
04:17 it really requires much earlier integration of and Geo mechanics into project scoping and
04:23 than what we really kind of traditionally in june in oil and gas projects
04:29 oil and gas a lot of times mechanics comes in once something has gone
04:34 and work in the radiation side. do we fix this here? Once
04:39 has gone wrong. Very likely you longer have a store. So we
04:43 to understand that and the risks for before we even start injecting um there's
04:50 great figure here on the side from of the nice overview articles um,
04:57 the science of carbon storage that sort sort of illustrates a bunch of these
05:02 of types of risks. So let put my laser pointer on just a
05:07 . I like to point. Um obviously in this you know we're thinking
05:12 injecting down into a reservoir unit. have the impact obviously of that direct
05:18 two plume. Um In the near we may have stuff related to um
05:24 of that through the C. 02 the inducing thermal stresses which could cause
05:32 in the near World War area. all honesty, I'm not gonna touch
05:35 heavily on this. We're going to more on the reservoir scale pieces of
05:40 gem mechanics. But it's really it good to really understand that. Um
05:46 that plume migrates, you'll have an in poor pressure in the reservoir potentially
05:52 then could lead to overpressure which maybe could lead to micro seismicity, small
05:58 . Um You could intersect a joint a fault which could provide a path
06:05 leakage pathway. Um And so what then if you start losing the containment
06:12 your cap rock as you pressure up unit, that reservoir unit, you
06:18 the potential to actually drive surface uplift to that overpressure. How do we
06:24 that? How do we monitor So as you can see there's a
06:28 of different things that can happen once start injecting fluid into the subsurface.
06:33 so really we need to understand everything goes into this before? We think
06:39 using somewhere as a C. 02 . So kind of expanding on
06:47 If we think about each of those keys to a successful project um If
06:53 look under the capacity, you're you're be asking questions like what reservoir pressure
06:58 your top steel, steel sustain um the infectivity of your reservoir? Does
07:04 reservoir flood depend on fracturing the And if so, what pressure is
07:07 that going to happen? Um If need to drill additional wells later on
07:12 the project, can we still drill ? Um What's gonna, what's gonna
07:16 to our pressures and stresses? So can drill those wells? And how
07:21 wells are drilled centers would be required on well worth stability models. Um
07:26 would be more thinking about your your development plan. Honestly, I'm not
07:31 I'm not gonna get heavily into well stability other than to sort of think
07:34 little bit about what goes into those of work. Um If we look
07:39 the containment side question will injection cause breach of the caprock seal? Um
07:45 there a risk of falter fracture Are we gonna have uplift? How
07:50 and how will the stress state vary injection? So we call that stress
07:55 and the mechanics and then on the side you know, is there going
07:59 be micro seismicity triggered? Where is going to be? Is it in
08:03 cap rock which could actually compromise your ? Is it going to be in
08:06 basement? Um Will those be potentially seismic events? Obviously that has a
08:13 big impact on um our our relationships the public and their acceptance of projects
08:20 this. If all of a sudden having damaged chimneys because of seismic
08:25 That's not a good thing. Um then can we observe if we do
08:30 fracture the cap, how are we to observe that? What are we
08:33 to look for? And will there uplift? And how are we gonna
08:36 that? So again, just another of peace and gives sort of,
08:45 not gonna still gonna go through this detail, but all of the various
08:51 parts of you're the questions that you're be asking about your potential store and
08:57 many of them do have pressure and mechanics as a piece of the,
09:02 the question. Um things related to integrity, things related to the site
09:09 . So that uplifts seismic activity. containment J mechanics is absolutely critical to
09:17 whether or not our C. 02 going to stay where we've put
09:21 Um things about how we're actually gonna our wells. And are we actually
09:28 have standing in any of our, any of our wells either in our
09:32 wells when we shut them in or we have to do brand production wells
09:35 those ones. Um and then Legacy most of the time we are going
09:42 places where wells have already been drilled some point in time, what is
09:46 integrity of those? Could those be pathways, in which case we need
09:51 understand the pressure that they may So there's not gonna be a lot
09:59 equations, I have been really careful that, but at the end of
10:03 day geo mechanics and poor pressure generally comes down to really one equation and
10:10 equation is thinking about how the change effective stress is resulting from changes in
10:18 stress and changes in pore pressure that in des formations, there's a strain
10:25 is proportional to the stiffness of our . So fundamentally all geo mechanics comes
10:33 to this and this basic idea um we will walk through a whole bunch
10:38 these to sort of talk about, know, where do we understand about
10:41 total stress is, what do we ? How do we understand the core
10:44 ? How do we understand the stiffness the strain all to allow us to
10:48 back to this change in effective So if we go back to the
10:57 beginning stress and pressure. So Geo deals specifically with stress and pressure with
11:03 being the part of the boundary forces supported by the fluid phase only.
11:08 And then effective stress being the net . Ad so if we look at
11:15 little diagram here we've got sort of plug of rock that we can use
11:20 an example. We have an axial coming down from the top. We
11:25 stresses coming into the side in this of radio stresses. Um and we
11:31 a pressure or pressure on the If we want to understand the stress
11:37 course acting on that rock, we the force acting over the area that
11:42 acting on. In this case we a plug. Um And then you're
11:47 see a lot of nomenclature in I try to be pretty consistent but
11:52 that a lot you'll see things change a lot when you look at other
11:56 geo mechanics pieces. Um Normally delta and delta sigma crimes will be types
12:04 stress changes that the PSR pressure You can also get stress changes from
12:13 in chemistry. Um Not really going deal with that, you've heard about
12:17 from some of our colleagues temperature changes also affects the stresses in Iraq.
12:26 big thing is that every single one these lead to volume changes and it's
12:31 volume changes that we need to quantify order to understand the so once again
12:42 just at the basic level, getting to some basic physics is simply the
12:48 divided by the area that the forces on. Um you know, in
12:52 subsurface that sends that that area and will be very large. Um When
12:57 take things out of the reservoir and the surface, we do work on
13:02 clubs. Obviously things change and we're at horses in smaller areas. Um
13:08 forces also get resolved on things like . So ways of thinking about how
13:13 forces are interacting with the various features the subsurface. Um most of the
13:19 you'll see in the US are going be S I pounds per square
13:23 Um If you're working out and basically rest of the world, you will
13:27 pascal's which is a newton meter square that's your assignment this. So the
13:35 thing that we want to understand if applied a force to a piece of
13:39 is what is the strength, which just the measure of the deformation.
13:43 its elongation or shortening under five So in this case it is simply
13:50 difference in the length of the material between two points. So the difference
13:57 it divided by the line. So , if we think about this,
14:06 happens if you do form and watch increased force. Typically that object will
14:10 in the direction of live load and in the direction of no load or
14:16 load. This allows us to understand the rock forms in this, it
14:25 us to define the stiffness. So is the slope of the stress.
14:31 the applied force over the area relative the strain, the amount of deformation
14:39 us in this case it's a confining pressure gives us the stiffness which is
14:44 to as the youngest module list. see that referred to as the.
14:49 it is simply, How much is piece of material going to deform when
14:53 have loaded up under a certain amount force. So this has been postulated
15:04 all the way back by hook. deformation is proportional to the load,
15:08 stress and inversely proportional to the That's exactly where this all comes
15:14 And you can see in most cases will see a lot of this working
15:18 the elastic space for everything and that's the slow for this this difference comes
15:24 is in this elastic space. Now frequently, move past that into plastic
15:30 prior to and fitting failure. But you will see most of the time
15:36 everything to find in the elastic In all honesty. Most Jamaican assists
15:41 to keep things as simple as Me being one of them and staying
15:46 the elastic space in terms of understanding formations really makes the math a heck
15:52 a lot of hair. So if take this and now think about how
16:01 locked in forms in different directions. gives us what we call the response
16:08 . So we can do this and this the the directive definition is a
16:13 ratio of expansion over shortly. Um thing to remember in that in geo
16:19 we work where compression is positive because in the subsurface and almost everything is
16:25 under compressive stresses. It means it all of our members positive most of
16:30 time, which is just a lot than dealing with negative numbers all the
16:34 . So this is a little different in the engineering disciplines where compression is
16:41 something to note. Um So here's ratio is actually defined as the negative
16:49 of how much it expands horizontally or amount that it compresses vertically.
16:57 another way to think about this because am not somebody who thinks in
17:02 I need a more concrete example is like to think of this as the
17:08 of squish to squash. If I my rock, how much does it
17:14 out? I'll come back to this to give a heads up the variation
17:23 numbers that you get for young for ratio are going to range between .5
17:29 one with sorry 2.5, wow, too early. Um so 2.5.
17:40 if you get all of your deformation the vertical direction is translated directly to
17:48 horizontal direction you want to put songs 0.5. Most rocks will sit between
17:54 of .22.4 is sort of the the range that we see most frequently interrupts
18:09 before we can move and really start about stresses. Let's think about
18:13 what we see in the subsurface. if we look at a simple plot
18:19 , looking at death on the world axis with pressure on the X
18:25 normal pressure, what we would call pressure is simply the pressure column of
18:31 . Most of the time in this will have varying salinity ease. Obviously
18:35 you're working in an offshore environment, will, you know, definitely have
18:40 before you get down into a coarse water. Overburden is the other end
18:50 on this block and that is the force exerted by the overlying sediments and
18:56 vertically oriented in space. And it simply the weight of accumulating sediments.
19:02 this becomes the primary driving force for and eventually the development of overpressure and
19:09 horizontal stresses. Most places that we to work. We'll talk about more
19:19 here in this green curve is the of the fluids within the rock.
19:24 the sediment pore space, we then a fracture pressure which is something usually
19:32 than our minimum horizontal stress equal to greater through the minimum bars all stress
19:38 will sit somewhere between pressure and over . The space in between the poor
19:47 and the overburden for the poor pressure any of our other principal stresses is
19:53 effective stress. It is essentially what rock these um and the effective stress
20:00 of Iraq really dictates its state of and the the deformation that Iraq has
20:11 coming up to the point that we before thinking about drilling a well,
20:18 this case you're gonna have a number other things that we need to be
20:22 attention to. The first one is pressure and that is the difference between
20:27 pressure, that column of water and absolute, the pressure that we see
20:33 the space. Sorry, this I didn't realize that those are all
20:39 of blend together. Um The top overpressure is the point first point where
20:45 pressure in the core space becomes greater that normal. And a drilling window
20:51 hear referred to is the space between court pressure and our fracture pressure.
20:57 is what we need to use in of a we call mud weight,
21:03 density of the fluid in our world in order to make sure that we
21:07 safely drill and not have fluid come our well because we're to lower the
21:13 and not lose fluid into the formation we have fractured it by going over
21:18 fracture pressure. So we've talked about and um and they are one of
21:30 obviously key pieces of all the mechanics . So we will work in,
21:36 principle stress space, which is going be the fact that we're gonna have
21:41 Ortho. Minal stresses them are all to each other. So this way
21:48 do not have to deal with shear during most of our work being that
21:53 is inherently a tensor. And I rather work with the simplest tensor I
22:01 . Now if you mark these is as one S. Two and
22:04 Three you'll have a maximum stress and and a minimum stress. But in
22:09 subsurface in the new york we have real sort of we have something working
22:14 us and that is the earth has a free surface and in a free
22:21 you can have no shear stresses. all our principal stresses will tend to
22:27 with one of those stresses being vertical the other two being horizontal, they
22:34 rotate in the subsurface but that is of the exception as opposed to the
22:39 . And we tend to work and about things in this principle stress space
22:43 one of our stresses is the vertical and then the other two we refer
22:48 as S. H. Men and . H. Max as our minimum
22:52 maximum horizontal stresses. And if we to move this into sort of a
23:01 geology concept and think about what it from a chronic point of view.
23:07 then helps us define what tectonic setting are in. Um And so in
23:12 faulting that's where the vertical stress is the largest stress and then the two
23:18 are lower than that with S. . Min the minimum horizontal stress in
23:21 minimum stress straight slip. That vertical becomes your intermediate stress. And then
23:29 thrust or reversible thing that vertical stresses now your minimum stress. So very
23:37 when it comes to how do we the stress state of the subsurface?
23:44 some of these we can measure some them. We cannot we can obviously
23:50 measure the vertical stress by simply integrating density of our column of rock.
23:56 that's what we showed on that last . We can always measure the minimum
24:01 that we have in a normal faulting that is S. H.
24:06 However, we will never be able measure the intermediate stress in the horizontal
24:12 here. And so this becomes really when you start thinking about if we
24:17 in strike slip or thrust faulting What we can understand of the three
24:22 so we can at most define two them, measure two of them.
24:28 after that we have to infer and bounds on what the what the third
24:36 is accepting thrust faulting wherein we can measure one of them which is the
24:42 stress because that is the minimum That is also the only one we
24:46 measure. So we can only put on what we think the two horizontal
24:51 are. So how do these stresses the interactions of them impact? How
25:04 see fractures in the subsurface. if we think about a block of
25:10 earth and we have drilled a well it. In this case we have
25:16 load, vertical load from the overburden then we have horizontal stresses in a
25:24 and a minimum direction. We've now fluid into that wild boar in this
25:32 , either because we are drilling a or because we are injecting into one
25:38 these formations and that gives us a column. In this case, I'm
25:43 that the static Mhm. As that increases, you will get to a
25:56 where you exceed the stress in some the formations when you do that,
26:02 generate a question. So now the question is, where is it actually
26:09 to go? Where is it going be oriented? So now, instead
26:13 looking at it from the side, looking down. So here's our world
26:17 . And so the vertical stresses coming and out of the screen at you
26:20 we have our two sets of horizontal . That fracture, which way is
26:31 to propagate in the direction of maximum strength? Why? So if we
26:39 about it, it needs To open against one of these dresses and it's
26:47 to be much easier to open up the minimum stress. So that fluid
26:53 actually opening the fracture this direction against minimum stress, which means it propagates
27:00 to that in the direction of the horizontal stress, it does not want
27:06 go the other direction. So that's about which election manufacturers are gonna
27:15 But what about you may have noticed were some variations in those horizontal stresses
27:20 you went through our overburden in that . And that comes from what we
27:27 the So if you remember songs ratio the ratio of squish to squash as
27:33 like to think about it, horizontal resulting from a vertical stress. So
27:43 happens in the subsurface when we do ? So if we have a block
27:47 this case of material with an original here in the square and in this
27:58 let's remove this cycling. So things start to to move and it can
28:02 deform. Once we start loading it the top, you will get an
28:09 in the vertical for the overburden active and it will deform both vertically and
28:22 . But in the subsurface we can't expand the battery. So what happens
28:29 the adjacent rock essentially pushes back and that lateral motion. And this is
28:37 generates off horizontal stresses in most places we tend to work. So most
28:46 mostly in normal and passive margin. situations, the vast majority of our
28:53 stresses are being generated by this person on our lives. If you are
29:00 in somewhere that has a lot of tectonics. So working somewhere where you
29:08 mountains being built or um somewhere like with the big strike slip system with
29:16 tectonics, then you'll have an added components. But this will still be
29:22 major driver in the horizontal stresses. what we see then, if we
29:29 at the variations in our formations in list of service is you will actually
29:34 stress difference between these formations. You see that sort of sketched out here
29:41 the differences in this, this red . Generally you're gonna see an overall
29:49 in stress with death as that overburden larger. But you do see contrast
29:56 units formations with those lower stresses are be much easier to fracture. And
30:04 depend on the fractures being contained within lower stress formations and not being able
30:11 grow up into those higher stress So for thinking about this, why
30:17 that be changing rapidly from one information another? And this comes down to
30:24 differences in the person's ratios of those . So a hypersonic ratio formation will
30:33 a lot more laterally, the amount it deforms vertically compared to a low
30:39 information. And we'll just have a higher stress. So typically shale formations
30:48 to be hyper sand ratio relative to formations. This works in our
30:57 This is what allows us to think putting a fracture into a sand unit
31:03 feel like it's hope that it's going be able to contain and be able
31:06 design it to be contained within the unit and not fracture into our bounding
31:13 . Um We use this in traditional and gas all the time. And
31:17 it comes to thinking about other sort fluid storage and fluid injection, it
31:24 incredibly important so that we don't compromise um app rocks, seals.
31:36 so everything we've been looking at on is in 3D and back and through
31:42 hard to structures up. So how we now take these three D tensors
31:50 stress and represent them in two So we want to think about the
31:58 on the resolution of forces onto a of known orientation. So we will
32:04 normal stresses onto any given plane. gonna call the sigma n which are
32:09 to that plane, and then shear which act parallel to that plane.
32:17 geometry dictates that for any given applied and plane orientation, there's gonna be
32:22 unique combination of normal and shear stresses are resolved onto that surface. And
32:27 can actually plot that now in two . If we look at just the
32:32 normal stresses and the shear stresses and are what are called Mordechai evidence.
32:41 actually really, really useful. You saw them previously in structural geology classes
32:47 something similar. Um we use them the time mechanics and they're incredibly
32:54 Um so these go all the way to the 1800s and it illustrates how
33:01 and stress transformations can be represented in really simple graphic. So as a
33:09 element is rotated away from the principal normal and shear stress components will always
33:16 on this. More circle are two stresses are shown here in blue,
33:22 this case, we're just looking at two dimensional ones. So the minimum
33:25 the maximum. So they're gonna plot is the blue dots right on the
33:30 with no shear stress. And then you move around, move that
33:38 the variation in the ratio of the to the shear stresses to the normal
33:44 will move along that circle. 127 . I am. What happened?
33:57 , we can hear you. Yeah. My computer. Just for
34:01 . So I have no idea just say the presentation it happens. Seeing
34:12 whole. All right. So one the things that's really helpful with more
34:22 is they give us a really, easy way to be able to think
34:27 . And and representing two dimensions for and thinking about whether or not we
34:33 going to cause for reactivation. vault reactivation is when the shear stresses
34:39 a pre existing fracture exceed really exceed strength of the fracture. In this
34:46 it's the friction coefficient and any cohesion gonna hold it together and cause it
34:52 move. Once that fracture moves, is released, the shear stress will
34:58 down to a level where it will moving and energy is released. And
35:03 reactivation energy is generally released as what think of as an earthquake. Um
35:09 that that earthquake can be large enough people feel, or it can be
35:13 small that it is only detectable, , really sensitive instruments. Um and
35:21 my laser pointer went away. What's ? Okay, so, man,
35:32 is released, Is it lagging for ? I'm sorry? Well, we
35:38 your cursor, but it's jumping. , because it's lagging really far behind
35:43 . Okay, I will try not use it too much. Then sometimes
35:48 point just gets really fussy when it's a big presentation. Yeah, it's
35:54 really mad at me right now, I don't know why, anyways.
35:59 basically, when we look, we have people see are more diagram over
36:04 on the left with sheer and normal on the two axes, and then
36:10 have two lines that I am, gonna call our failure to syria,
36:16 one of them is going to be intact material, and the other one
36:19 for fractured material. And then we're have our more circle down below this
36:25 is a three dimensional more circle. it has that intermediate stress. Don't
36:30 about that, you can you can them either way. Um really the
36:36 that you need to understand is understanding two dimensional one. Um And as
36:42 moves as soon as that more circle either of those failure lines. For
36:48 , intact material is when you will to rock. Either through slip on
36:53 pre existing alter fracture or by breaking intact material. And on the left
37:02 is just an example of how you actually induce those, which we will
37:07 at what you do on a more when we change things in the sub
37:13 , maybe. There we go. , so we can use the more
37:17 to help us predict whether or not are going to have for reactivation.
37:23 we will now plot are more circle that effective stress. So that remember
37:28 stress is the total stress minus or within the within the rock. That's
37:35 the rock actually feels. And when do this, increasing the poor cluster
37:41 our rock causes are more circle to to the left, which moves it
37:47 failure. And what you can see that for a wide range of fault
37:53 which is being plotted in that red on the more circle, which is
37:56 pull to the fault plane. If think back to your um your structural
38:04 , you can then see which orientations faults are potential. Actually critically oriented
38:11 the stress state stress field and are to be reactivated by increasing the pressure
38:18 our formation. So simple logic would taken to apply. That would include
38:35 will always believe the fault reactivation and would always lead to stability. If
38:40 simply move your your more circle directly , your body have no change in
38:47 size of it. That is the between your minimum and your maximum
38:53 However, what actually ends up happening the subsurface and with rocks with rocks
39:00 and natural materials is that that decrease pressure from a depletion standpoint for injection
39:11 if you're increasing the pressure changes the stresses, which basically is telling you
39:18 the difference between the minimum, the stresses, that means that you end
39:25 with a change in the size of more circle in addition to shifting it
39:32 and right. And that unequal change stress is produced generally by the four
39:39 effect. We're not gonna get into in detail at this level, really
39:45 you need to sort of know and carry going forward and thinking about this
39:50 that changes in pressure are not going impact your vertical stress and your horizontal
39:57 to the same amount. There's a another parameter in there that's the poor
40:03 parameter. That is going to tell that how much they change by which
40:07 change the size of your more So what happens when you push a
40:20 to being what we call critically So exceeding that fractured stability line that
40:29 story is that Hey, Stephanie, I think we've gone as far as
40:36 want to go with this. Um you want to see the rest of
40:42 let me know and we'll post the of the video but I'm going to
40:48 it now so I could get back doing my job. So now I
40:54 to pull up the next uh hold . Have to make sure that I
41:04 the right windows here. Yeah. . So we'll move to the next
41:15 which is seismic velocities by the Did you have any questions on on
41:26 video? Yes. I have a question about the the injected C.
41:36 . So what face will it be we inject the C. 02?
41:41 . Well it depends how deep you . But usually for carbon storage they
41:48 to be deep enough so that it's super critical fluid. So it's above
41:54 critical point. So it will be liquid right more. Yeah. But
42:01 mean that also depends on the temperature so forth. But I would say
42:06 a liquid. Yes. Yes. so you mentioned the temperature. So
42:11 we want to inject the C. to deep reservoirs, the temperature will
42:17 as well. So is there what's preferred uh death or covered storage?
42:27 . You know, I'm not sure how deep you can go. Um
42:32 seems like the pressure effect is more than the temperature on the volume.
42:38 the deeper you go, the more of C. 02 you can put
42:43 a given pore space. But of the pore space tends to decrease with
42:48 also. So it's a big trade between the seal, the porosity of
42:53 reservoir etcetera. But uh generally you to get as deep as you
42:59 Um There are also other issues. Some of the C. 02 dissolves
43:08 the water. Uh Some of it be trapped as residual gas as it's
43:15 . Uh So it doesn't even have be in a physical trap and some
43:20 it starts to solidify, it reacts the rock. So there are a
43:26 of different things going on all the time. And and and so these
43:30 things were just starting to understand and about. Thank you. Okay,
43:40 let me share again and I want share seismic velocities. So one of
43:59 reasons we've been emphasizing rock mechanics and and so forth is because this is
44:07 controls velocities. Right? The velocities controlled by the elastic module. I
44:14 uh so that's where the rock mechanics in and the elastic module. I
44:20 controlled by the pressures. The confining , the poor pressure. So getting
44:28 to uh physics one. Uh We talk about transverse waves are longitudinal
44:37 So when a transverse verse wave the motion is orthogonal to the direction of
44:47 . And so shear waves are transverse and longitudinal waves, uh the particle
44:55 is in the direction of propagation. here for this uh analogy analogy to
45:02 compression wave, you have a compression which then moves through the rock and
45:08 there is a compression, there's an rare faction or attention associated with
45:16 And these uh this particle motion moves the rock and that constitutes a
45:25 So now drawing this um going to one, uh we'll draw this as
45:33 propagating through a three dimensional medium and will look at what we call infinite
45:41 volume elements. So we divide the rock up into a uniform uh series
45:50 cells. Infinite test simile, small cubic. And if we propagate a
45:58 all wave through that piece of there will be zones of compression and
46:04 of tension. Now interestingly, if look at these volume elements, if
46:11 look at their change in shape, will notice that they are lengthening or
46:18 but they're not getting any wider. And this is what Ellen was saying
46:24 the video, you know, you squeeze longitudinal e on a piece of
46:31 in the earth and the surrounding rocket is also being squeezed, pushes
46:39 So the net uh forces or stresses on one of these horizontal planes
46:46 they cancel out. So uh it's . we talked about the laboratory experiment
46:54 we put the sample in a rigid , right? That prevents the material
47:01 getting wider. Okay, so um course the because of the poison
47:08 as Ellen was saying the the stresses this boundary will change there will be
47:17 where we're more compressed because the rock trying to get wider. But it
47:23 it just can't do it because the rocks are pushing back. So when
47:29 propagate a compression all wave we have change of shape and we also have
47:35 change in volume Two things happen on other hand, when I propagate a
47:42 shear wave through the rock, you'll we change the shape of the volume
47:48 but the base times height is the . So we haven't changed the volume
47:55 those infinitesimal volume elements. So the wave only involves change in shape.
48:05 the bulk module asses, the resistance the change in volume. So a
48:11 wave. Since it involves a change volume and a change in shape.
48:17 P wave depends on the bulk modules the sheer modules, the shear
48:22 on the other hand, there is change in volume. So it doesn't
48:26 on the bulk modulates. It only on the sheer modules. Another view
48:36 the same thing. Uh So let's one volume element as a function of
48:43 . So these are different snapshots in and this particular volume element you will
48:49 is uh being stretched or squeezed as function of time. So that's the
48:59 passed. And that's the way form seeing, we're seeing compressions and
49:05 So peaks and troughs on our way as that volume element is being stretched
49:13 squeezed. Now while one volume element being squeezed, other volume elements are
49:20 be stretched. And this is what making things very complicated because in a
49:29 oh elastic permeable medium, there are in the rock. So while I'm
49:36 and squeezing the rock frame, I changing the fluid pressure. So I
49:42 volume element, I increase the fluid . So here I have a high
49:48 region here I have a low pressure . What is the fluid gonna want
49:53 do? Fluids are always gonna want go from high pressure to low pressure
49:59 want to equal a break the So as this wave is passing then
50:05 get fluid motion. Um And this called B. O. Flow
50:12 I. O. T. Uh and the flow of the fluids will
50:18 out of phase with the solid because the fluid gets to this stretched region
50:26 wave has moved and that may by time or even before it gets there
50:31 may become a zone of compression and fluid may move back. So you
50:37 the fluid is uh it's not a compression. The fluid doesn't have time
50:43 move from the compressed region to the region. And so depending on the
50:50 of the wave, the fluid may longer distances or not. If it's
50:57 very high frequency wave, the fluid essentially be frozen in place before it
51:03 a chance to hardly move at It will get a signal to go
51:08 to where it started. So we different amounts of fluid flow as a
51:15 of frequency. And as I mentioned , it is fluid solid friction.
51:22 is the primary attenuation mechanism in sedimentary . Well, actually, in all
51:31 that that have fluids in them. ? So um you have an attenuation
51:42 depends on frequency, that means you're have a velocity that depends on
51:50 And so body waves are uh inherently it. And higher frequencies will be
52:00 . In fact, than lower You could think of that as being
52:04 fluids essentially being stiffer. In the of very low frequency, there's plenty
52:10 time for the fluid to move. so the rock is more relaxed when
52:17 fluid can't move. And it's only it must resist the compression that it's
52:27 because it can't escape. So the frequencies are also higher velocity now in
52:36 shear wave, it's different because there's volume change. And so the amount
52:43 B. O. Flow associated with shear wave is less and this is
52:50 it's been observed that in propagating through reservoirs, for example, p waves
52:57 attenuate a lot more than sheer Uh They'll attenuate more because it's a
53:03 liquid mixture, usually gas and water um that the water is free to
53:13 by compressing the gas. Now there's type of flow that occurs which is
53:19 very microscopic flow. So um this called squirt flow. And so what
53:27 is some pores depending on their orientation preferentially squeezed, and water will be
53:35 out of those pores to go into open pores. So that's a micro
53:42 kind of flow and that affects both p waves and the share waves.
53:52 , as I mentioned in the uh we want to relate the physical
53:58 of the rocks given their environmental conditions the elastic properties. And again for
54:06 passage of seismic waves, we're going treat the velocities to first order as
54:12 elastic. Um So we're gonna ignore uh at this point in the
54:21 Um These elastic properties. Then the modulates. The sheer modulates and the
54:29 then determine the acoustic properties. P velocity, shear wave velocity and the
54:35 elastic properties affect the attenuation of the wave and shear wave uh Q.
54:42 called the quality factor. It's one the attenuation. So this is the
54:47 of attenuation in the p wave and reciprocal of attenuation and shear wave.
54:53 of course it's three dimensional combination of things and density which produces the seismic
55:03 . Okay, so as I said , the P waves depend on the
55:07 modulates and the sheer modulates as well the density, whereas the shear waves
55:12 only on the sheer module asse and density. And this is why the
55:19 wave velocity is strongly dependent on the . And this is why we can
55:25 p wave reflection seismic data as a hydrocarbon indicator because the sheer module asse
55:33 not affected by the fluids unless your are entirely disconnected and highly oriented.
55:40 in a permeable rock, the sheer asses independent of the fluid properties.
55:47 as I change the fluids in the , I'll change the bulk module.
55:51 change the density some. So I have a minor change in the shear
55:55 velocity, but the biggest effect is the bulk module asse. And so
56:02 is the basis for direct hydrocarbon Okay, so in the laboratory,
56:12 the old days, uh the way used to uh measure velocities would be
56:19 put transducers on either side of a and we would have to know the
56:25 of that sample. That sample could in a pressure vessel. It could
56:31 put under pressure. It could also a piston on it. So you
56:36 be burying the uni, uni, stress for example. Um And we
56:42 use a digital oscilloscope. Uh Well before the digital oscilloscope, we would
56:49 an analog oscilloscope and it would generate signal that would go through an
56:56 That signal would drive a transducer. transducer would create a wave in the
57:02 . It could be a P wave shear wave depending on the type of
57:07 . The wave propagates through the rock received by another transducer. I'm sorry
57:14 pulse generator generates the signal. It the oscilloscope, tells it to start
57:20 and then goes through the amplifier. sorry, I have a completely
57:27 Let's start over the pulse generator triggers oscilloscope and it also triggers, drives
57:35 transducer. And so it sets a of a certain shape. And that
57:40 travels through the sample is received by transducer which generates a current which is
57:48 and goes to the oscilloscope. And the early days we would then take
57:52 picture of the waveform later on, would uh be able to digitally digitize
58:00 way form in the oscilloscope. Transfer to a computer. Nowadays, instead
58:05 an oscilloscope here, you have a to do to do things. So
58:12 are the kinds of pictures we would in the old days. This was
58:15 digital oscilloscope. So you see these are the samples of the wave
58:20 . So here's the input pulse. that gives us T zero. And
58:27 can see it's not exactly obvious uh where T. Zero is. And
58:34 we have our recorded waveform and there's noise here. Uh This is our
58:42 wave and you can see that there's superimposed noise. So measuring that P
58:47 is not always very obvious. And is the share wave. Uh If
58:55 P wave is strong in the shear this week then you get interference between
58:59 two which makes measuring the shear wave time a little bit ambiguous. Now
59:08 do you pick, remember we're taking time a time from the trans from
59:14 transducer to the other. Where do pick the arrival for example on this
59:20 wave uh What do you do pick first peak? Depending on where I
59:25 the arrival, I'll wind up with different velocity. Right, so that
59:31 an ambiguity. It would be nice you could watch the wave propagating across
59:37 receivers but typically that's not the way is done. Typically it's just what
59:42 call a pulse transmission. Okay, points of discussion how accurate and how
59:55 our laboratory measurements. So um any from the peanut gallery, what do
60:06 guys think? Do you think um measurement is precise? Yes, I
60:17 it's precise. Yeah. And so of all, what's the difference between
60:25 and precise accurate means? How right it precise means? How repeatable is
60:33 ? So you can be precisely Right. So repeating the measurement 10
60:40 in getting the same answer doesn't mean right, it just means that you're
60:45 a precise measurement. Alright, so measurements are precise. If you could
60:50 the noise of course that this noise variable in front. That could introduce
60:57 little bit of error. Because you're maybe on slightly different parts of the
61:04 . Uh So there is some error you know that's typically small and um
61:10 could uh if you average many way you could average that out for
61:16 Um But is the measurement accurate? what do you think? I feel
61:27 it just kind of depends on the that you're working with. I feel
61:32 maybe it'd be more accurate with others others. Yeah. No, no
61:37 absolutely right. It depends very much the sample. And of course how
61:42 we define accurate? Right. So accurate is it doesn't represent the velocity
61:50 the rock in C. Two in earth from once it was sampled.
61:57 . So think about it, what happened to that rock as we've sampled
62:02 and brought it to the surface? first thing that happens is we drill
62:08 core. Right? And so we're the rocks in the core under a
62:16 schimmel stress, right? Because it's rotating drill, right? So we
62:23 the rock and not all rocks are court if if a rock is very
62:28 or if it's already got natural the core may just fall apart or
62:34 the rock is very unconsolidated, it just slide, if it's like a
62:39 it will slide out of the the barrel right? Um So uh we
62:47 the rock under stress then we brought to the surface. And in fact
62:53 you watch a core and they bring to the surface and they lay it
62:58 on the floor you could see the expand. Why is it expanded because
63:07 brought it from high confining pressure to surface pressure. So the rock is
63:16 when you bring it to the surface that can be a plastic deformation.
63:22 that defamation may not be completely So then putting the rock in a
63:28 vessel and pressuring it back up may bring it back to where it
63:34 Also fluids are leaking out of So we may be changing the mix
63:40 fluids in the rock and with different in the rock. You could get
63:44 chemical reactions for example. Um You if um If I if I take
63:53 shell that was previously mixed with salt and then I saturated with de ionized
64:01 for you know very uh fresh zero per million in a cl for example
64:10 water may react with the clay minerals than the brian reacted with the clay
64:17 . Um If I dry the rock you know sometimes they put the sample
64:24 an oven and they dry off all water and then they put water back
64:28 or they put oil in? You all of this? We're changing the
64:32 and then we we already spoke about . Sis you pressure it up,
64:36 pressure it down, you pressure it . So in fact um even for
64:44 piece of rock the measurements are not accurate. Now another question is that
64:50 of rock representative of what's in the ? Well, first of all you've
64:57 all the rocks that don't core. right. So within the interval you've
65:05 you are already preferentially sampling those samples hold together. Also where engineers decide
65:13 core is uh is biased by where think reservoir rocks are. So your
65:20 samples are probably over representing reservoir rocks under representing other rocks. So not
65:29 is the sample itself is the velocity measure on it. Perhaps not representative
65:35 the N. C. Two. the rock sample itself may not be
65:40 . It may be a biased sample its its dimensions are an inch or
65:47 . Whereas a seismic wave may be tens or hundreds of feet.
65:53 So uh you know that relating a physics measurement directly to what the seismic
66:02 is seeing is in my opinion a task. Okay so our rock physics
66:12 useful we've already established. They're But are they useful? Well yeah
66:23 would imagine. Yeah because we may do we do all this?
66:28 Why do I study rock samples? ? Why are they useful? Because
66:41 would tell us like how how do explain it? How good it
66:48 How like the rock um reacts to certain. I literally just had a
66:58 . I don't know how well I what you were getting at. I
67:01 to let you say you're absolutely We could study how the rock the
67:07 reacts to changes in pressure temperature. could look at a suite of rocks
67:12 see a dependence on composition. We see how it changes as we change
67:17 fluids. So yes, we can the systematics and we could try to
67:23 the physics of what's happening and we calibrate that in the laboratory. So
67:30 though the laboratory measurements are not good predictive purposes, they're very good at
67:35 us understand and have an expect expectation what's going to happen. So I
67:43 we're gonna find again and again that , we're gonna and this is true
67:50 all the sciences, but in rock , a lot of what we do
67:54 wrong, but we do it anyway it's useful. I just uh,
68:00 just learned last week one of the we'll learn about and I mentioned it
68:05 on was gas men's equations, gas equations allow you to change the fluids
68:12 the fluid properties in Iraq and study the rock modulates will change and therefore
68:20 the velocities will change. And we this every day. I mean,
68:26 it's widespread. The use of it widespread and actually one of my most
68:32 papers used gas mains equations. two of my most cited papers used
68:38 mains equations and nobody objected to their . And you know, they went
68:44 scientific review and everything else. And learned last week that uh leon Thompson
68:51 proven that Gas men's derivation was wrong Gas Men's equation is wrong, Which
68:59 just a startling fact and a very one. We're going to study gas
69:04 equations. There are in fact more equations, but much harder to
69:11 And typically I don't even talk about equations in this class. So,
69:19 , and yet even though it's it's been used all these years and
69:25 never been so grotesquely erroneous and what predicts that people suspected that it was
69:34 , right. For one thing, think there are compensating errors in the
69:38 people apply it. Uh, but , uh, being wrong is
69:45 as long as what you're doing is and important concept. Okay, now
69:55 really try to gear this class to that are going to interpret velocities and
70:03 reflection amplitudes and therefore seismic impedance is terms of the factors controlling the seismic
70:14 . So, having that understanding of systematics in my mind for an interpreter
70:21 more important than in being able to out the equation that will tell you
70:26 how things change, especially because none these equations are precisely correct.
70:34 So, um, I am going spend a good bit of time talking
70:40 the factors that affect compression, wave . And first of all we have
70:46 ology. And what do we mean lethality? Well, means the type
70:52 rock. Right. And so how we determine? How do we give
70:58 name to Iraq or how do we Iraq? You know, what makes
71:03 particular rock in Arcos? Arcos or Ortho court site? Right, so
71:09 a limestone part of it is the . So in our coast would be
71:15 telepathic rich rock. An Ortho courtside be a pure court sandstone. Uh
71:23 course the limestone is primarily calcite. ? So composition is part of
71:30 but there's also texture. The difference a sandstone and conglomerate and a silt
71:37 could be entirely due to grain You could all those rocks could be
71:44 quartz, for example. Um so that's back to one with
71:51 Next is the pore space. And loosely calling that porosity because it's the
71:59 of ferocity that matters, but it's the type of ferocity. And then
72:05 we start talking about disperse it effects attenuation, then the permeability kind of
72:11 in as a second order thing, uh from if we're just looking at
72:18 velocities. Uh, the amount of and the shape of the ferocity or
72:24 two died in factors. And that's I spent a lot of time talking
72:29 that earlier in the class. Then have a number of things that are
72:35 related in general as a tendency velocities in depth in detail. Maybe
72:43 You could get deeper and move from high velocity rock to a low velocity
72:49 . But overall the trend is to velocities to increase with depth. And
72:56 what happens as we increase with Well, usually the differential pressure increases
73:02 as a consequence the effective pressure I noticed that Ellen and her presentation
73:09 draw a distinction between differential and effective . Most people don't. So what
73:16 differential pressure? The difference between the pressure and the poor pressure? Um
73:23 uh with the exception of abnormally high pressures. With the exception of geo
73:31 . Um The effective pressure generally increases depth. Then the degree of with
73:39 also increases with depth. So, are these factors? Well, number
73:45 is aged typically, the deeper you , the older the rock. Not
73:50 you could have thrust faults. You have overturned folds for example, but
73:56 age increases with death. That means been more time to cook the rock
74:02 put it under pressure and have re or whatever else. Just generally as
74:09 rock gets older, it's had more to get cemented up and to become
74:14 harder rock. Uh And again, shin uh can decrease, increase with
74:23 . In fact, when you get deep, semente shin becomes one of
74:27 primary mechanisms for porosity reduction. But it's primary effect is to glue the
74:35 together and then especially shallow you have and compaction. We talked about rearrangement
74:44 grains. We also talked about defamation grains. So these things in
74:51 the pore space is being reduced as compact the rock. Uh So all
74:59 depth related things. Another factor are poor fluids in the rock. A
75:07 rule of thumb, you could take one to the bank. If I
75:11 brian with gas, the velocities In fact, that's not theoretically always
75:18 . I could mathematically create Iraq where I add gas, the velocity will
75:24 , we'll talk about that later, I've never actually encountered that and I've
75:30 at a lot of velocities in my . Uh So uh the poor fluids
75:35 the rock are a big factor and why we have direct hydrocarbon indicators.
75:42 are also the environmental factors. We about temperature. Now temperature doesn't really
75:50 the grains very much the solid material the exception of organic matter, but
75:58 minerals typically are not affected greatly by temperature, but the fluids are so
76:08 can vary with temperature. Uh the of the waves I mentioned dispersion
76:16 So frequencies a factor the geometry of experiment relative to the natural anisotropy of
76:22 rock. The anisotropy could be in crystals, or it could be in
76:29 lamination, zor the layering of the . So getting back to with
76:39 there is a general tendency that soft have the lowest velocities. Sand stones
76:47 shells would be intermediate. Carbonates on average would be higher velocities. These
76:52 hissed a grams of just a random of laboratory measurements. Just measurements that
76:58 to be available in the literature. , about 50 years ago when this
77:03 done. Um Then higher than carbonates to be your igneous and metamorphic rocks
77:12 uh your evaporates then tend to be highest velocities. Uh This this is
77:20 rocks in the upper crust of as we get deep in the
77:26 uh the igneous rocks are going to uh are going to be much higher
77:35 . And so you could take what called. The 80% financial limits.
77:40 , you could, you know, the width of this hissed a gram
77:45 you have 80% of the samples are that with these are the fiduciary
77:52 And again, you could see this tendency here, but also notice that
77:57 a lot of overlap. In sand stones, I would pill pull
78:02 up up to here. In fact and Dolomites can go up to
78:08 Uh of course the gran it's igneous could be much higher than everything
78:19 Okay, so here are those history's and uh these are just uh some
78:26 rock types showing you ranges for those rock types. Okay so we're gonna
78:40 with the simplest kind of rock that could think about constructing. And in
78:47 it's not even a rock, it a suspension of grains. So the
78:55 aren't even touching yet. That's why is an easy equation. And so
79:01 we want to plot the velocity of suspension of courts in water as we
79:08 the volume of courts from zero. that should say x courts. Let
79:12 fix that. Well now I'm not do it now during the presentation.
79:20 ex courts goes to one and you use I'm gonna ask you to do
79:27 in your spreadsheet. And so use bulk modulates of courts of 38 as
79:36 giga pascal's as we did before. use the bulk module asse of water
79:44 uh say 2.5 giga pascal's. So a salty water And let the density
79:53 courts be 2.65. And the let's to make it easy, let's make
79:59 density of water one. So I'm stop sharing and Stephanie if you would
80:12 your Excel spreadsheet. I could look your shoulder and and don't hesitate to
80:19 questions. And can you see my ? No no not yet. I
80:31 to re share. You can see now. Okay, So a few
80:52 , what is the sheer modulates of suspension zero. What is the bulk
80:59 of the suspension is given by Woods , which is the same as the
81:04 average. What we just did in spreadsheet, The density comes from the
81:11 balance equation as we did, and the velocity is just square root of
81:16 over density. Alright, so there's solution for you. Alright, moving
81:26 , get this out of the way . I'm not sure how to do
81:35 . It won't move. Okay, these are Faus empirical relationships if you
81:41 see that. Oh there we And this was done in the early
81:49 . And when sonic logs were first available and uh foust noticed a
81:57 he noticed that velocity increased with I'm sorry with age with age of
82:06 rocks and velocity increased with death. he used he just empirically he was
82:14 to fit all the velocity data he with just a single concept, constant
82:23 uh h 216 power times depth to 16 power. So where did
82:28 16 power come from? Well, the same time Gasman was doing his
82:38 . And when he uh theoretically took packing of spheres and calculated the change
82:46 velocity with pressure as he put that of spheres under more pressure. Um
82:53 contact area increased. So the grains less compressible And he found the velocity
83:02 with pressure. So if you translate to depth using typical gradients, it
83:09 out for the theoretical equation that it also to the 1/6 power. Uh
83:17 . one problem here, there's no on uh ferocity. Um So uh
83:27 is assuming all rocks at the same and the same age have the same
83:34 . Uh What he did have abundantly . We're resistive itty logs at the
83:42 and the resistive itty, if you're brined saturated is in a given
83:48 Ology is highly correlated to porosity. he substituted the resistive itty log and
83:54 would have to be the deep resistive beyond the invaded zone. And uh
84:00 found this relationship. And to this we use this relationship when we don't
84:07 sonic logs. So we have unreliable logs to create pseudo sonic logs.
84:13 this type of relationship. So here gas man's relation. So he had
84:24 depth to the 16 power. He had this factor and this is kind
84:30 the proxy for age or porosity. he has the grain properties like the
84:38 modulates of the grain and the poison's of the grains and he's got density
84:45 there and he's got porosity in So you could think of this as
84:49 somehow the degree of with indication and being the depth by the way,
84:55 is when people talk about gas means , this is not uh the gas
85:02 equation and this was a different equation came up with. So you can
85:11 the general tendency. These two just arbitrary velocity versus depth profiles. And
85:20 is this overall trend that velocity increases depth, but with the little logical
85:27 , uh it's it's it's not a increase with depth. Now, these
85:37 are the curves that fast fit. don't have the data points to
85:43 but these are the trends he came with. So if you take his
85:49 age to the 1/6 power time step the 16 power uh This is the
85:56 he came up with. So at given depth, the older the
86:00 the higher the velocity that makes And for Iraq of a given
86:05 the greater the depth, the higher velocity. Now, in the early
86:16 of well logging, um we didn't direct porosity measurements, we didn't have
86:23 logs, we didn't have density The first logs were just resistive
86:29 And if you wanted to get water , you needed to know the
86:33 If you had the resistive itty and porosity, you could calculate the water
86:38 . So when sonic logs were first , their main use was to determine
86:45 porosity of the formation. And the is because velocity and ferocity are
86:54 All else being equal. The the the porosity, the higher the velocity
87:01 the mid-50's Wylie Gregory and Gardner came in 56 the year I was born
87:08 the way. Um They came up an equation like this and fitting their
87:16 where uh it was a reciprocal volume or volume fraction waited. Reciprocal
87:23 So one over the velocity of the is equal to the ferocity divided by
87:29 velocity of the fluid plus one minus divided by the ferocity of the
87:36 which they call the matrix. Um we have a relationship between velocity and
87:46 . Now this looks like a theoretical . It looks it looks a lot
87:50 woods equation, right? We could had K here and it would have
87:54 woods equation. Uh but theoretically that's right. So this in fact is
88:02 an empirical equation. And in fact in fitting the data, you'll use
88:09 matrix velocities that are not representative of minerals and sometimes you'll use fluid velocities
88:17 are not represented. And by the , one should not use this equation
88:24 calculate the effect of hydrocarbons. For , if you put hydrocarbon velocities in
88:31 or a mixture of brine with this won't do the fluid substitution for
88:39 , it will get it wrong. . So this is purely a theoretical
88:44 and think about it. This equation possibly work for shear waves because uh
88:52 velocity of a share wave is gonna uh infinite. I mean it's going
88:58 be zero. So this is gonna infinite here. This reciprocal. So
89:03 time average equation can't work for share . Um And uh it's it's just
89:13 accidental that it fits some data. If if this were a homework
89:21 I would ask you to write this in terms of slowness is right.
89:27 What is slowness? Slowness is the of velocity? And they call
89:32 they call this reciprocal of velocity. If measured with a sonic log is
89:38 sonic transit time. So it's how it takes the wave to travel one
89:44 . So the units of that are microseconds per foot. So this would
89:49 delta T. The sonic transit time equal to porosity times the transit
89:55 the fluid Plus 1 - Porosity Times Transit Time of the Solid. And
90:02 you had multiple constituents instead of one porosity, you would have volume
90:08 courts times the transit times of Court's volume fraction limestone or calcite times the
90:16 time for calcite etcetera. You would write this all as a linear
90:22 And it looks like it's the transit in the fluid plus the transit time
90:27 each solid material, which is not way waves work. But anyway.
90:33 people use it. Uh The equation proven effective for clean or sand stones
90:41 high pressure. So there is a set of rocks for which this equation
90:48 really well for Um and it's got be granular rocks um if you recall
90:57 discussion of ferocity and the effect of ratios on velocities, this is not
91:03 work for equant pores and it's not work for very flat cracks.
91:11 It tends to work for Iraq's with aspect ratio on the order of
91:20 Now we've already seen a velocity porosity . We weren't as terms, but
91:28 we have density versus velocity, that's velocity ferocity transform cause porosity is
91:36 I mean density is linearly related to . Um So, um now we
91:43 two equations relating uh ferocity to velocity they don't agree. So which one's
91:52 ? Well, the answer is time equation is right for some rocks.
91:58 relation is right for other rocks, average equation usually deep well with ified
92:05 sands Gardner relation more for poorly lit rocks. So the original measurements that
92:18 , Gregory and Gardner made uh the worked for a range of uh ferocity
92:27 . But they realized early on that didn't work for some very highly porous
92:35 rocks uh essentially empty shells, uh cell ish, isse shell
92:43 uh shells uh that deviated from the . So not only well identified um
92:54 Rocks under high pressure, but also is less than 30, So because
93:06 one velocity transform matches all rocks, not surprising that there are a wide
93:16 of equations to relate velocity to Prasit . And these equations really depend on
93:23 rocks that the authors were dealing So we have the widely equation,
93:31 clean, uniform meteorology, uh water and high effective pressure for the wildly
93:41 . Uh Slumber came along in Remer and Gardner, different Gardner uh came
93:49 with this equation, which they said an improvement to Wiley's equation And the
93:55 had two branches for very low for under 37% and then for very high
94:02 is above 47%. Um It turns that this equation as we saw when
94:11 were discussing density, this equation tends be for the most lit defied
94:17 This again is purely an empirical but it acts as a very practical
94:23 bound. Remember we talked about the and the voice bounds well, in
94:30 , we we've never encountered rocks that near the void bound. Uh Rocks
94:38 to be softer than the the void . That's the maximum possible velocity you
94:44 have. Um But we don't get near there. The Ray martin Gardner
94:50 is really your practical upper bound and has the the solid fraction squared times
94:58 velocity of the solid press, plus times the velocity of the fluid.
95:07 , if you get to very high is your rock starts to lose cohesion
95:12 it starts to act more like a . This is another empirical equation,
95:20 not the wood equation. What you here here in the denominator is not
95:27 . If these were case, that be the would equation. But what
95:31 are our road V. P That's the plane wave modulates K plus
95:36 thirds mute. This is K. the fluid because there is no
95:41 but this is K plus four thirds for the solid. So that's saying
95:47 don't have a pure suspension that's close a suspension, but it's um it's
95:54 a little bit of rigidity, which sense because um you see divers walking
96:00 the ocean bottom and they're kicking up cloud of dust of dust but they're
96:06 sinking all the way in. So shallow unconsolidated sediments have some small
96:17 So this is the ray murdock Gardner . Whereas the wily equations are linear
96:24 transit time. Here we have sonic time here, the roemer equation is
96:30 . And so they have the branch porosity is less than 37%, they
96:36 the branch for porosity is higher than . And what to do in between
96:42 they just interpolate between the two. depending on, you know, as
96:48 get closer to 47%, you use of this equation as you get closer
96:54 37%. You use more of this most significantly over the range of velocities
97:01 we usually try to estimate porosity Where Wiley was linear, The rain
97:08 Gardner equation is nonlinear in transit time that range. So what effect does
97:18 have? Well, look at this of rocks here, these samples,
97:28 rain martin Gardner, excuse me. wily equation works quite well with a
97:33 velocity very close to the velocity of . So it works for these
97:40 but doesn't work for these rocks to . These rocks have to use a
97:46 matrix velocity and that matrix velocity is physical. You could have a pure
97:52 sandstone and yet you have to use velocity. Why? Because the relationship
97:59 some curvature, which Ray martin Gardner capturing and this is the high porosity
98:10 for shallow marine sediments and it matches more or less some ocean bottom sediment
98:20 , the Royce band would have been envelope, It would have, you
98:24 , been way over here. So pulling it back to slightly higher velocities
98:31 uh, the wood equation, because the development of some rigidity.
98:40 now, by changing the matrix you could change the velocity ferocity
98:49 So, at a given ferocity, sandstone tends to be slower than a
98:57 than a limestone tends to be slower a dolomite. Um similarly, at
99:03 given sonic transit time, that would a lower porosity. If you're a
99:09 and a much higher ferocity if you're dull moment. Now, the other
99:13 that Raymond and Gardner do and I you you should not do it with
99:17 wily equation is they could do fluid by changing the velocity of the
99:24 And even though this is purely an equation, for some reason, the
99:31 you get is not too bad, least it's in the right direction.
99:35 may not be quantitatively precisely correct, um it's it's gets you in the
99:44 of the right answer. So that's advantage over the walleye inflation, You
99:49 use it for fluid substitution. so that's what we're gonna do
99:57 we're gonna compare velocity ferocity sand So we have a few, we
100:04 the Gardener sandstone equation, we have wily time average equation. We have
100:11 wood like equation, that's where we em instead of K. And we
100:17 the Ramayana Gardner equation. So what would do is I would make a
100:23 of porosity and using these values, would then use these different equations and
100:33 and calculate um uh the velocity versus for each of those equations and then
100:42 them and compare them. So we'll sharing. Now can you see my
100:58 ? Yes. Okay, where were ? Okay, so coming back to
101:16 gardener equation, we saw this one . If you plot the log of
101:24 against a velocity on a log So it's a log log plot the
101:31 equation becomes linear and as you can it's a rough average of other rock
101:38 and it divides sands and shales. I showed you data points where it's
101:43 almost the dividing line. If you're this side, you'll be a sand
101:47 that side of shell. So by this equation for all rock types,
101:53 could be getting the reflection coefficients Uh but as a rough first
102:00 it's pretty good. So for a starting model for inversion, you
102:05 use this and then the inversion will to a nearby answer. Um Anomalous
102:15 are the evaporates rock salt is abnormally velocity for the given density and and
102:24 is abnormally high density. Now we about the critical porosity model before,
102:38 we're saying that around 40% ferocity things uh lose cohesion and become more
102:48 Like so this black curve here is relation. So we were looking at
102:56 wood like relation, it would have it up a little bit. Woods
103:01 is a true lower bound, that's low as you can get. And
103:06 points violate that, you start to about maybe some experimental error there,
103:13 I think it's pretty good. It makes a pretty good lower
103:17 Uh now if we look at the porosity at which things uh tend to
103:28 at that lower bound, we could could pick a porosity here and say
103:36 And anything below 40% is gonna have degree of with ification anything above that
103:43 going to be unlit ified. So will call 40% or in the vicinity
103:48 40% the critical porosity. Now, we take this module is here we
103:57 a velocity, we have a Prasit so we have a density. So
104:01 have that modular list and we just that module asse be the void average
104:07 courts with that value. I can a line here and that's called the
104:15 porosity model and that's going to be close to the Ray martin Gardner equation
104:21 it acts pretty much as an upper . So the critical ferocity model is
104:27 upper bound um, on for the rocks. So you could get points
104:36 in between. By the way, is the wily equation here and here
104:43 have a number of points which are lines, They come along straight
104:47 These are actually points that were all on the same sample. And the
104:53 thing that was changed was the effect pressure. So the effective pressure reduced
104:59 ferocity and increase the velocity. So lines are uh for the same
105:08 And so you can see why it's hard to estimate porosity just from velocity
105:16 it could be over a very wide . Right? So at a velocity
105:22 4000 m/s, I could be what porosity or it could be 25%
105:29 So that's those bounds are so wide it's not practical. However, if
105:35 know the degree of with indication, I say well yeah, I have
105:39 fully liquefied rock then I could predict porosity pretty well. Okay, so
105:48 looked at this before uh here the porosity model says the dry module asses
105:57 to the modulation of the solid material one minus the ferocity, divided by
106:05 critical porosity. Right? As porosity to zero, this goes to ones
106:10 you go to the mineral modulates and same thing for the bulk modules.
106:16 , these are for the dry we then have to add the fluid
106:22 we would use gas men's equations to that. Okay, so what does
106:31 critical porosity models say about the P V. S ratio of the
106:41 rock? It turns out the V V s ratio. If I take
106:53 Vp equation and I divided by the . S. Equation, right.
106:59 . P squared is K plus four over mu I'm sorry, K plus
107:05 thirds mu over rho right. S squared is mu over rho So
107:12 P B S squared, divided by . S squared, cancels the
107:19 Okay, so B P B S over B. S squared equals K
107:24 mute plus four thirds. Did you me with that? Okay, so
107:33 over mu controls the V P S ratio right? V P uh
107:41 divided by the S squared for the rock equals k overview for the dry
107:47 plus four thirds now. So what K overview for the dry rock?
107:55 see what happens when I do that . Of the solid times. This
108:01 by K. U mu of the times that the porosity term cancels
108:08 So K dry over mu dry equals . Solid divided by mu solid.
108:15 what the critical ferocity model says is dry rock has the same B.
108:21 . B s ratio as the mineral up the rock. And it's now
108:29 model is purely hubristic. It's not based on matching data. And yet
108:36 saw it made a very good upper . And it turns out that in
108:43 , The a dry courts, clean Quartz Sandstone has a v.
108:50 v. s. ratio 1.5. Pure Court says the V.
108:54 B. S ratio of about You know, poison's ratio on the
109:00 of 0.1. So the critical ferocity gets two things right, It gets
109:06 rate the dry frame V. P . S ratio. That's going to
109:10 important later for fluid substitution. And gets that right for sandstone. I'm
109:17 saying it's right for other rocks, it happens to be right for sandstone
109:23 it acts like an upper bound on the velocity, practical upper bound for
109:28 the velocities can be. Okay, now these are laboratory measurements where we're
109:43 at a mixed with ology, it's longer a pure mythology and uh varying
109:52 clay content and what you see is we saw this before as we add
110:02 to a clean rock, we reduce porosity and as we add quartz grains
110:09 a clay sediment uh we reduce the going this way, Right? So
110:16 saw this kind of V shaped curve there's a minimum ferocity, right?
110:23 you look at the compression module asse not exactly the doing that but it's
110:29 same idea that as you mix clay courts as you're reducing the porosity that
110:37 modular increases. But then you add clay so you're taking away courts and
110:45 module is decreases. So this is nonlinear thing. Let me try to
110:49 the pointer here, I'm sorry. we are. Alright, so that
110:56 some intermediate intermediate mixture where adding clay increases the module asse because I'm decreasing
111:05 ferocity. But while that's happening while plane, while the plane wave module
111:12 increasing the shear modular sustained pretty much same. And if this were a
111:22 assignment I would ask you to think hard about this and try to come
111:26 with an explanation. I'm not gonna you on the spot and make you
111:30 that now because uh there isn't an explanation. So we'll let that
111:41 Okay, now I've talked a lot the poor shape and its effect on
111:51 And we've distinguished pores which are more from cracks which are very flat.
112:01 one way we could study this is could add cracks to Iraq, you
112:07 take a low porosity rock and you crack it. One way to crack
112:12 is to heat it up to a high temperature and then quench it very
112:17 and the rock will crack when you that. So, here's an
112:23 this is a dry rock and it's axial pressure. So it's not a
112:30 pressure, it's just a piston pushing on the cylinder. And for the
112:36 gay bro, very low porosity, , high density, low porosity for
112:42 gay bro, as we put pressure it, the velocity increases.
112:48 Because we're probably closing any horizontal cracks are orthogonal to the uni axial pressure
112:56 is being applied right? It's it's close those cracks and the velocity
113:05 Now we're gonna introduce a lot more . And we're gonna uh heat cycle
113:15 and introduced severe cracking. And two happen. Uh The rate of change
113:22 increase of velocity with increasing pressure is , at least at low pressures.
113:31 that's one thing that happens. But thing that happens is we never get
113:36 to an equivalent velocity. The velocities always lower. And the argument here
113:44 here, we're closing cracks very A lot of these micro cracks that
113:51 as we increase the pressure. They And then all of them that we're
113:56 close close, but not all of close, there's we you know this
114:02 is not an elastic phenomenon, It's completely reversible. Right? So uh
114:09 rock still has a lot more cracks that rock. But we've closed all
114:14 horizontal ones here. Right. Well , we pretty much closed the horizontal
114:20 , but there are a lot of cracks that have been introduced.
114:28 so, time to play the hypothesis . But let's see, I think
114:37 both are entitled to one more So let's take the break now and
114:42 reconvene at four o'clock if you You could uh you could chew on
114:48 plot and try to explain the But uh we'll reconvene at four.
115:02 , so this plot the velocity is a granite says the low velocity of
115:08 ferocity. Rock is measured as a of time. This is calendar
115:17 So they take the rock, they its velocity and they wait and they
115:21 it again and again and again and velocities keep decreasing. Um Any explanation
115:39 it be maybe because of like because kind of went over in the beginning
115:46 with age like compaction and segmentation. , but remember this is not geological
115:55 , This is time in the And the velocities are decreasing. So
116:04 is changing in the rock sample and is a dramatic change in velocity.
116:11 ? Big change of velocity in a porosity. Rock. Well, what
116:18 be changing with time? So I say this granite is a sample for
116:28 world. So when we take it the deep layer to the surface,
116:35 adults, the confining pressure. So generate some crack inside and so lower
116:44 velocity. Yeah, that's a good . Um And the other thing that
116:52 be happening, it's possible fluids are out of the rock. So the
116:57 that develop are more compressible. So I said if you put gas in
117:06 rock the velocity always decreases. air is a gas, right?
117:11 if water comes out of the rock is replaced by air then the velocities
117:18 gonna decrease. Okay, so this a very strange one. It's another
117:35 . So it's a low porosity And um they've made different kinds of
117:45 . Number one. They made a on the saturated rock with the poor
117:51 being zero. As the confining pressure , that means as the confining pressure
117:59 increasing, the differential pressure is increasing . But how do they keep the
118:05 pressure at zero? They let the drain out of the rock.
118:13 so fluids are draining out of the so the poor pressure doesn't increase.
118:19 do they measure this? They actually a tube into the rock connected to
118:23 poor space? And so they could they could determine that the poor pressure
118:29 an increase. And they're comparing uh saturated rock, that means the rock
118:38 fully saturated with uh with water but water is free to leave as a
118:47 as the rock is being squeezed. like squeezing a wet sponge and the
118:53 comes out right? But there's still that remains behind. And this is
119:00 velocity of the dry rock. Now they also look at the case
119:11 zero differential pressure. They set the pressure equal to the external pressure.
119:20 external pressure being the confining pressure. you see that as they as they
119:28 the confining pressure, the velocity still . That means the differential pressure is
119:36 equal to the effective pressure. The effective pressure is actually increasing as
119:43 confiding pressure increases, even though the pressure remains constant. So this is
119:53 waves. This is for share waves share waves a little bit different when
120:03 . At first the velocities are lower when saturated, but very quickly the
120:12 become faster when saturated. And a case with the effective pressure not being
120:21 equal. So how do you explain behavior? At least the saturated versus
120:37 . So, I'm gonna let you on this. You notice that high
120:51 , the saturated in the dry becoming equal, essentially equal. Right.
120:58 something's happening with pressure to reduce this mm. So is it possible that
121:25 the high pressure, the high external uh closed the and course. So
121:35 the close together. I think that's good hypothesis that as we increase the
121:44 pressure, I mean the the effective is increasing dramatically, right? Because
121:50 poor pressure zero. And when we're fluids out of the rock, the
121:55 we're squeezing them out, we're closing flat pores. So uh that's what's
122:02 . We're closing the flat pours Why should then the flat pours?
122:07 should the velocity be higher when we fluids in those flat pours than when
122:15 dry? What do you think is there? So, I think because
122:23 with higher because of the V. . P BP is also considered the
122:33 also a function of the shared So we have water inside will increase
122:39 velocity of BP. Why do you the velocity because of the dry?
122:50 mm. It is Does the saturate has higher share modules than the
123:01 Okay, well, let's start with shear wave then. Maybe that's a
123:05 bit easier to understand for the shear ? The dry rock for most of
123:12 pressures except for very low, the rock is faster than the saturated
123:18 Why would that be? Well, explanation would be that the density is
123:26 and the sheer module asses the So the velocity is higher. Does
123:33 make sense? Can you say that more time for shear wave velocity?
123:43 dry if if the rigidity is not by the fluids, then the dry
123:52 would be faster than the saturated rock a ship for share waves.
124:00 remember, it's sheer module is divided density. So the dry rock has
124:05 lower density. The sheer modulates is same. The velocity will go
124:14 Now, obviously, there's something else to even for the sheer wave because
124:18 very, very low pressure. The rocks are slower than the saturated
124:28 So, I'm gonna argue that in very flat Poors having fluid in those
124:38 resist the defamation of those pores. primarily resists compressive deformation. But even
124:48 the case of shear waves, it resist shear deformation. So somehow it
124:57 um it requires uh stress to remove fluid from those cracks. Right?
125:08 takes work to do that. And the fluid for however much resistance it
125:16 to moving out of those cracks. therefore uh resisting the compression. You
125:24 what I'm saying? I'm gonna argue those flat pores are easier to close
125:31 dry than when saturated. And for the dry rock, you see
125:36 much bigger changed of velocity with You buy my explanation. In
125:48 the fluids in those flat cracks are shear too, because if sheer is
125:55 those cracks, if they happen to oriented such that the sheer emotion is
126:01 the cracks, The fluid has to out, and, you know,
126:07 not perfectly mobile, there's gonna be gonna take effort to push that fluid
126:14 of the poor. You see what saying? So to some extent,
126:19 though extensively the poor pressure is zero on a micro scale, the uh
126:29 pressure must be increasing some degree because fluid doesn't effortlessly leave you see my
126:39 ? Yes, I do actually. like uh what's a good analogy?
126:47 like uh squeezing a tube of right? It takes a little bit
126:55 pressure to squeeze that toothpaste out. come out but it still requires some
127:00 to do it. Okay, so this case the effective pressure wasn't equal
127:10 the differential pressure. But here is case where it was. So this
127:17 a sandstone. And uh here we we're increasing the external pressure,
127:28 And um the F Bar here is differential pressure. So the differential pressure
127:39 the external pressure minus the internal fluid . So here as the external pressure
127:47 increasing the differential pressure is increasing also you can see the velocity is going
127:55 . But then they say, okay allow the fluid pressure to vary and
128:02 , you know, have a gauge the fluid pressure and a pump on
128:08 fluid pressure such that we could maintain fluid pressure constant and they're increasing the
128:18 pressure. I'm sorry the fluid pressure not constant, The differential pressure is
128:24 . So as they raised the external , they're raising uh the fluid pressure
128:34 enough to maintain the differential pressure And if the differential pressure is constant
128:41 it's 2000, the velocities are the here. It's 1000 P.
128:47 I. The velocities are the same . The fluid pressure is made equal
128:53 the external pressure so the differential pressure zero. And no matter how high
128:59 external pressure the velocity stay the same notice as the differential pressure increases,
129:06 velocity increases. So this is a case where the the effective pressure is
129:16 to the differential pressure. In this the effective pressure was higher than the
129:24 pressure but in this case they're Uh These are a couple of other
129:35 , higher balon and last one. uh these are similar lines of constant
129:43 pressure. So you see as the pressure increase or as the differential pressure
129:49 velocity decrease. But if they hold differential pressure constant velocities are more constant
129:57 not exactly right. In fact at low differential pressure you can see there's
130:06 big change of velocity with change in pressure. So here, at higher
130:13 pressures the differential pressure is almost equal the effective pressure. Not quite.
130:20 a slope on here but at low pressures it's nowhere near being uh the
130:29 pressure. Okay, so this is from Gardner Gardner and Gregory's famous paper
130:39 I suggested you read. And here have instead of velocity we have slowness
130:47 time microseconds per foot versus ferocity. these are average measurements. So they've
130:56 lots of wells at different depths so shallow to deeper. And this is
131:07 time average equation Using a matrix philosophy 18,000 ft/s. And they fit the
131:17 values pretty well. You could see were until we reached the point they
131:25 this being fully compacted. So if under compacted here, you deviate dramatically
131:33 the wily time average equation. Now strange thing here what is the matrix
131:42 velocity that's being used? It's not . Alright, time average equation.
131:51 18,000. That's not pure course. probably as we were saying with the
131:59 martin Gardner equation. The range of was such that that transit time happened
132:05 work. But that's it's an empirical . It's not theoretically equal to the
132:13 time. Of course. So here we're not fully lit. Ified were
132:19 compacted. These these rocks are Then they reach a point where they're
132:25 fully compacted. You get this knee bend and then you tend to follow
132:31 time average equation. And so here could compare average measurements. These are
132:46 coast U. S. U. . A. I think it was
132:49 17,000 measurements that they had. And solid curve is the velocity versus depth
133:01 to the data. So this is a smooth fit to all the data
133:06 they had. Now if they take sand pack and they just pressure it
133:13 to the equivalent differential pressure as well log measurements, these were,
133:19 log measurements, they don't get that of increase. So just changing the
133:27 , they take a stand with that and they just change the pressure and
133:33 get a much smaller increase of velocity depth. So there's much there's more
133:43 in velocity with death then can be just by pressure. So you're having
133:51 mechanical rearrangement of grains, you're having shin uh then you reach a point
133:59 you're almost parallel to the time average here. Not quite, it's still
134:05 steeper trend. So it's not just changes, there's more going on,
134:12 semente shin defamation of grains et Okay, this one's gonna take a
134:22 bit of explanation and I'm gonna ask to explain what's going on or come
134:30 with a hypothesis to explain what's going . So um they are going to
134:38 the same formations in a uh in basin compared to the same rocks in
134:50 uplifted area. So in a more area. Okay, so first we'll
134:56 to the basin and they look at velocities versus depth in lime stones and
135:05 fit a straight line to it. that's the limestone. Regression line,
135:13 then look at their shells versus death they get that line, They then
135:23 that well, if things are, know, interpolated between the two.
135:28 I have a mixture of limestone and , say I'm 60% limestone, 40%
135:35 , I would combine these two trends I would get that regression line.
135:41 this is all in the basin. why did they go to this uh
135:47 ? Because they went to the mountain they found rocks with this composition 60%
135:56 . But Shelly and they got that velocities which were higher than their limestone
136:07 line at the same depth. The rock which should have been slower,
136:12 faster than the limestone. Okay, hypothesis to explain what happened.
136:39 she'll Mhm. And it's at the of the mountain, would it be
137:06 No, because fractures would decrease. . Okay, never mind.
137:20 So, I'm gonna give you a word hint history, sis. And
137:50 what what they're arguing is that these in the basin were buried this
137:58 They were then uplifted and they kept velocities. So these rocks were originally
138:07 here before the uplift. Alright. actually as they were brought up,
138:15 would, you know, it's not elastic. So it doesn't go to
138:20 . Right. They get brought up velocities don't get slow, but they
138:27 have been slowed a little bit. in fact, these rocks, you
138:34 , this is kind of a minimum that would have occurred because these velocities
138:40 actually a little bit lower than they have been here because as they've been
138:46 , they uh they lost some right? So actually they might have
138:52 even deeper. So this is kind a minimum estimate of the amount of
138:57 that occurred. Okay, now shells pretty relatively d for mobile compared to
139:11 , noticing those sands, we have knee, whereas shells tend to just
139:17 deform. And so if you plot transit time versus death, this is
139:26 what you see. So this is are from, well logs,
139:33 well, logs and they go to clean what they call clean shells zones
139:39 are pure shale almost. And they those velocities versus depth and they get
139:45 well defined line like this? This called a normal compaction trend. And
139:54 rocks, the poor pressures are increasing the weight of the overlying pore
140:02 Now, what would happen though if certain depth? The pore pressures are
140:09 able to equip vibrate and the and fluids have to bear the weight of
140:15 rock as well as overlying fluid. that case the poor pressures would be
140:22 . So the at a given depth the same confining pressure, the poor
140:27 increases. That means that the effective , the differential pressure is going to
140:33 . So the effective pressure is going decrease. So what would that do
140:38 the velocity that would lower the And that's what they see if they
140:45 pressure into shell. This isn't from well. So they plot their shell
140:52 and they follow this normal compaction trend they hit what they call the top
141:00 overpressure. This is where you have high pore pressures and the velocities
141:07 So these velocities at great greater depths similar to the shallower depth velocity.
141:15 the last time this velocity was seen at 4000 ft/s. Right? So
141:22 velocities are slower than they would have at that depth if you did not
141:26 the geo pressure. And that's a of recognizing high pore pressures. High
141:31 pressures can be dangerous for drilling. could cause blowouts if you happen to
141:37 a permeable sand uh in high Uh that fluid is gonna, you
141:44 , force its way up the well . If you haven't waited up the
141:49 enough. And if there are hydrocarbons , then you get friction with all
141:53 movement. You get a spark and get a blowout and people die.
142:00 , detecting these high pressures is Alright, so here's an example plotted
142:09 velocity. The previous one was in time. So, abnormally high transit
142:16 . This is velocity. Same Normal compaction. And then you go
142:23 these thick shell intervals and you get velocities. Now within that shell,
142:29 may have some non shells, You could have sand stones or you
142:35 have carbonates. So you get some and velocity, of course, with
142:41 , with ology, but overall your are much lower velocity. Uh This
142:50 showing the same thing with conductivity. , so this is this kind
142:58 it's an indirect proof that we're seeing shale deform the pore space to
143:03 Uh you get higher pore pressure, get you force the pores open,
143:08 get better conductivity. So not only the sonic velocity get lower, but
143:15 resistive itty gets more conductive associated with same top of pressure. Okay,
143:28 of the same now, um if have a permeable permeable sand, you
143:36 , you have here, you have geo pressured shell, that means there's
143:41 permeability barrier. Uh These would make good seal, but if you get
143:46 sand in the interval, you could to bleed off the pressure, especially
143:52 the sands. If there's a pathway the sands to the surface, for
143:57 . So, permeable layers can help you back towards the normal compaction.
144:05 didn't quite make it back here. , so how does this uh affect
144:16 programs, for example? So here a normal compaction trend here are velocities
144:25 seismic interval velocities and you see they're more or less at the uh
144:32 compaction trend than they deviate. So slower than they should be. So
144:39 that deviation, you could predict the pressure. So here, they're predicting
144:43 uh poor pressures, that's an artifact the sample rate, right. This
144:49 should have been measured maybe there, because this is blocking from seismic velocity
144:56 that undershoot there on, on velocity too slow is probably an artifact.
145:03 ignore that. But, uh, , you're seeing uh, from this
145:11 here at this point, you're seeing predicted poor pressure. Now, remember
145:18 Ellen was saying earlier today, you to be between the pore pressure and
145:25 fracture gradient and the fracture gradient, close to the overburden gradient, but
145:30 don't want to fracture the formation. you do, you'll lose your drilling
145:35 into those fractures, right? And have drilling problems. So you want
145:41 keep the ports, you want to the mud wait above the poor pressure
145:46 hold the fluids down, but lower the fracture pressure. So in this
145:51 , maybe the fracture pressure is out and they had plenty of room.
145:56 these were the actual mud weights they and they kept the mud weights above
146:02 predicted uh, poor pressures. here, there's a little cross,
146:10 ? If that's real, that could been a problem. Had there been
146:14 permeable sand there? But if it just shale, there, probably not
146:17 problem. Now, you don't want keep the mud waits too high if
146:22 too over balanced. What you can is push fluids away from the
146:28 So, any hydrocarbons that the borehole be pushed away and you may not
146:32 realize that you had a discovery your logging tool may not have the penetration
146:39 see those hydro carpets. Also if mud waits too high, it really
146:43 down the drilling and you could have stability problems so you can try to
146:49 the mud late what mud weight as as it is safe to keep the
146:55 way? Alright, Show This Alright, so here was an example
147:02 the mud way actually was less than predicted poor pressure from seismic uh
147:11 The drilling engineer didn't pay any attention what the geophysicist would have said.
147:17 that chance and this well was drilled so they got away with it.
147:27 , now another thing that varies with is the degree of anisotropy. So
147:37 we have a rock sample and the are measured parallel to betting which is
147:44 , in perpendicular to betting which is for the shear wave. They look
147:51 two different polarization of the shear So the particle motion is in direction
147:57 parallel to the bedding or it's orthogonal the bedding. Right? So be
148:04 propagation direction or be it um polarization you're parallel to betting you're faster.
148:13 Ellen was saying you're fractures will develop the direction of maximum horizontal stress.
148:21 this could be betting or this could been relative to the direction of maximum
148:27 stress. If you're parallel your if you're perpendicular, you're slow.
148:34 the difference decreases with pressure. I need a hypothesis. The
148:51 Yeah, but why does the anisotropy ? You're right. It has to
149:05 with poor closing. But I need little bit more explanation than that.
149:13 I will say that is due to poor. So diplo the foreclose,
149:21 were no more national tropics so they closed. So what how would closing
149:30 change anisotropy? What would have to true about those pores? The poorest
149:42 um orient specific orientation direction? So if your poor shape is flat
149:54 if it's in and if the poor is parallel to betting as you would
150:00 in a shell for example. And betting planes if shales are fissile.
150:07 ? So if we uh if we those, those bedding planes, if
150:14 force them closed, we can reduce facility, thereby reducing the anisotropy.
150:21 closing essentially it's closing pores that are elongated parallel to betting. Okay,
150:37 is an interesting one shear wave We're increasing the hydrostatic pressure and the
150:51 are increasing. That suggests to me the yeah, differential pressure is
151:02 If we're water saturated, we have slowest velocities. If we're dry,
151:07 have the fastest velocities. And if kerosene saturated, we're in between on
151:15 other hand, that's share waves on other hand, from p waves,
151:18 you're dry, your slowest you add , you're faster and you add brine
151:26 your fastest explain because kerosene has a viscosity than. No it's got a
151:57 than brian has got a lower density it has a lower compressibility. I
152:03 a higher compressibility, it's got a bulk module asse. Okay, so
152:10 the share waves are not affected by fluid then this is entirely a density
152:20 . On the other hand, kerosene uh less compressible than air but it's
152:30 uh more compressible than brian. So we're seeing a fluid substitution effect based
152:38 the bulk modulates change and the bulk change must be bigger than the density
152:44 . This is the density change. in the p waves we're seeing a
152:48 modulates and a density change. So bulk modulates effect must be bigger.
153:04 um I'm now gonna let's see it's maybe we'll start tomorrow with
153:13 So let me skip this, we'll back to this. So here this
153:26 from map coz course notes out of , he has effective pressure is confining
153:33 minus poor pressure. What he really is differential pressure here. So the
153:38 axis is differential pressure. And he's p wave velocities to shear wave velocities
153:47 he's comparing water saturated to dry and notices different kinds of behavior here,
153:59 and dry. Give the same trend V. V. P.
154:03 B. S. No difference here a big difference at low pressure between
154:12 and dry and the pressure decreases in cases, the pressure is decreasing.
154:18 here we have a huge difference we have smaller difference, oddly
154:27 on this guy, the saturated shear is faster than the dry shear
154:39 Okay, so why these different What would be the difference between this
154:50 and this granite? Why the huge here? And a very small,
154:57 small difference here? And why does difference decrease decrease with increasing pressure because
155:19 is more compacted? Yes, granite harder than limestone. It's lower
155:28 probably than the limestone. Alright, , uh you're seeing a bigger effect
155:34 fluids because you have more ferocity right , why does that affect decrease with
155:42 pressure? B because of her Right. You're closing flat pores and
155:59 leaving behind? Only the pores that couldn't close. Right. And so
156:05 pores are less compressible. The remaining here are less compressible, so less
156:10 the fluid effect. Okay, this guy's Ott. This stolen
156:19 the saturated shear velocity is faster than dry. How could you explain
156:37 Mhm. I'm trying to remember. feel like I know why, but
156:46 don't know why because something about Not sure. So, something about
157:02 ? Dolomite can have very flat intra porosity due to the re crystallization from
157:12 , right? You're changing the shape the crystals and that could introduce ferocity
157:20 ferocity may not be in a lot it may be disconnected. So if
157:26 disconnected porosity, uh fluid in those pores can resist share compression if they're
157:38 right orientation. If the fluid can't out as you share the rockets gonna
157:43 to squeeze that fluid and the fluid get out. So this may be
157:48 case where you have enough disconnected porosity the fluids actually help resist. Uh
157:56 the the sheer and so the rigidity the fluid saturated rock is actually higher
158:02 the dry rock. And so I'm invoke as a hypothesis. I don't
158:09 the answer, but I'm gonna guess this rock has disconnected ferocity. It
158:14 to do with the way dolomite ferocity created, I think. Alright,
158:20 about this rock soul? And often , Very little pressure effect. No
158:28 between saturated and dry. How do explain that low porosity? Yeah,
158:40 , essentially. No porosity. so um that's all, that's all
158:50 today, By the way, this , remember Moscow saying the bigger that
158:56 the more cracks you have and the amount of time it takes to get
159:07 this assam tone up here is related the crack shape. So here you
159:12 only very flat pores and so they right away here, you have a
159:19 distribution of poor shapes. So you to get to higher and higher pressures
159:24 close some of them. Okay, again, tomorrow we'll do the same
159:31 we did on saturday. Last We'll start at eight, We'll finish
159:37 four and we'll work we'll work through . Is that right? Is that
159:42 we did? I'm trying to Started a Okay work through lunch.
159:51 , so we'll see you tomorrow at
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