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GEOL7324 Rock Physics - Day5 11-04-2022
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00:02 Yes, yes, I'm here. couldn't figure out where the button
00:08 Okay. So first of all I to apologize. My um location is
00:17 by workmen on every side doing different . So if it gets too
00:23 let me know and I'll try to a closet someplace, but if it's
00:28 , I'd prefer to do it from desk. So um, last time
00:34 were talking about fluid properties and before proceed, are there any questions by
00:41 way? Um, you tie? , was the recording I posted to
00:48 ? Did it finally show up? yet. Okay. I did something
00:57 when I tried to move the recording dropbox, it started playing and I
01:04 know. We'll have to discuss that another time how, how I'm supposed
01:09 put things in Dropbox. I haven't that for a while. Okay,
01:15 about that. Fortunately it was a recording. You, you tie took
01:20 of most of it. All Stephanie, any questions from anything we've
01:28 so far? Um Not really. everything seems to be making sense.
01:36 because I'm a great instructor and you're great student. So of course that
01:42 happen. I just feel like a of this stuff is um, I
01:47 know this is like the most I practical class I've taken so far.
01:51 I'm enjoying the material. So it's sense. I'm hoping that means
01:55 you know, you know how to . Brownie points. That's really
02:01 Um, so let me say a more words on oil properties and then
02:07 do some exercises also to make sure get a good grade in this
02:12 we're going to go over some practice . Okay we'll be doing some of
02:19 uh today and tomorrow and next I'll ask you how's the exam I'm
02:25 work and you want me to go campus for that or is it just
02:27 be like online? Like we've been well since it's just you and
02:32 I don't see any reason why we do it online and you'll just um
02:40 you know we'll we'll be online together case you have any questions and when
02:44 done you'll just email it to Okay. Yeah. Okay.
02:52 Oh hold on hold on. I keep forgetting. I think maybe
03:00 do this is a Wednesday night right? I and I think you
03:05 have to come to campus wutai when the final? I mean you tai
03:12 you tie? Yes. Sorry, you say the question again when when
03:17 the final? I think proctor Right. It will be um November
03:26 . And what day is that? a Wednesday? And usually on the
03:31 is from 6 to 9 p.m. By time X, flexible you can we
03:38 change it. Okay. Um I'm to do it at another time if
03:45 and you you and wutai agree on time but you would have to come
03:50 campus. So so I take that . I'm sorry about that, I
03:54 which program I'm in. Okay. . I was just curious because like
03:58 dr Thompson and doctors out, they kind of sent it to me and
04:02 I just sent it to them whenever was done with it. But
04:05 I can go to campus, that's . Well if they did it then
04:09 don't see why I couldn't do So I'll just email it to you
04:14 you'll send it back to me. grade it and give it to.
04:18 I want you to do it during , you know an appointed time.
04:25 if if Wednesday 6 to 9 is for you, I'll make sure you
04:31 it before six and I want your by nine. I want to email
04:38 to me and you know, wait me to confirm that I received
04:42 We don't want any errors in Right, Okay. Yeah. So
04:47 I receive it then then it's Okay. Alright. We'll do it
04:53 way. So let me just make I have that on my calendar.
04:59 Utah It's the Wednesday the 16th. . I will send you a reminder
05:08 day before. Um And how many classes do we have? So we
05:18 tomorrow and next friday. Yeah, what I thought. Okay.
05:24 And by the way, Stephanie, while you're preparing for the final,
05:29 feel free to email me any questions have and I'll get back to you
05:34 . I'm good at responding to That's one of my better qualities.
05:43 , okay. So to summarize fluid july uh this is a good summary
05:52 . It covers brines and uh so see there's a wide range if we
05:59 at the variation versus temperature a people often uses they use brian properties
06:06 S. T. P. Standard and pressure and you know, that's
06:12 the surface and they assume uh you , desktop and they assume uh pure
06:22 . And so that doesn't really work we could get very saline waters in
06:29 subsurface as we've seen. And the asse increases dramatically with salinity. So
06:37 I have if I'm very saline and very high pressure you could see I
06:42 , you know, I could almost the module asse. Right. And
06:48 so there's a wide range there of module is so that needs to be
06:52 to account of course those ma july the average except you know at low
06:59 at low temperatures most of the time brian becomes more compressible as you heat
07:06 up. Remember, water is a bit unusual, It expands when you
07:10 um It also becomes at low temperatures pressures. It also becomes more um
07:19 me, less compressible as you increase temperature, oils have a wide range
07:26 low temperature and pressure. Um They to be more like brian's near the
07:33 as you get deeper to higher they get more and more like
07:39 Um The major factors controlling the oil asse, aside from temperature and pressure
07:45 the gravity of the oil. Low is heavy oil, high gravity is
07:51 oil. And also then the gas ratio, the amount of dissolved gas
07:57 the oil. So that gives you fairly wide range for oils. And
08:03 you have, you know, and are much more compressible right, Especially
08:08 high temperature. Now, if you to just guess, and you had
08:13 brine module asse and you had a module asse if you had to pull
08:17 number out of the air, unless at very low temperature. Just assuming
08:24 oil module asses about halfway between the modulates and the gas module asse you're
08:31 gonna be too far wrong, so that at least will get you
08:35 the ballpark for gasses. The pressure important uh Much more compressible than
08:45 But the module asse does get significant low temperature and high pressure have for
08:53 . Um We could pretty much ignore module asse. It's um when we
09:00 about dry rocks, we we just that the air is so compressible that
09:06 we just assume the module asses Alright, so then we went over
09:13 last time, we uh mixed ma and if we have a mixture of
09:21 phases. Uh And we pointed out woods equation is the same as the
09:30 average and the Royce average is a weighted reciprocal average. So this is
09:37 equation. Of course the density is linear average, right? But the
09:44 ass's a reciprocal sub and therefore the can be extremely nonlinear. As we
09:53 , suppose we're just mixing gas and . There are only two components
09:59 So the volume of water is the saturation and the volume fraction of gas
10:04 one minus the water saturation. So the volume weighted reciprocal some and gas
10:12 , especially when gas is very So low pressure gas, it's essentially
10:18 on off switch. Uh It's still significant that a little bit of gas
10:25 the modulates a lot. So it , if the, if the rock
10:28 is compressible, it will drop the a lot, a little bit of
10:34 . But the higher the pressure the higher the pore pressure, the
10:38 linear the effect is you can see nowhere near being linear. That would
10:42 a straight line between there and there's still a lot of concave cavity
10:46 it, but it's far more linear for a very compressible, like
10:57 Okay, so let's look at some , logs, uh here we have
11:01 gamma ray log, this is pretty responding to the volume of clay.
11:06 high gamma rays are your shales, gamma rays are your reservoirs. So
11:13 would be considered clean reservoirs. If look at the resistive ITty log uh
11:20 shells have low resistive ITty, you into the top of the sand and
11:25 becomes high resistive ITty you go further the sam sand and the resistive ITty
11:31 way down even lower than the shells into the shale. The resistive ITty
11:37 back, go into a sand, goes down again and in the underlying
11:42 it comes back up. So what's these resistive Itty variations? Well just
11:49 the gamma ray log and the resistive log, it's not obvious what's causing
11:55 because we don't know the porosity. this high resistive Itty here could just
12:01 low porosity sandstone. Whereas this is porosity sandstone. Um Of course with
12:09 density log it gives us a sense the ferocity now. Right, so
12:13 shells are high density, the sands low density but the top of the
12:20 is even lower density than the bottom the sand. So if this high
12:25 ITty were due to low porosity from mass balance equation it would be high
12:32 but we see its low density. we interpret, so we interpret this
12:37 being a porous rock that's filled with and it's very porous because the effect
12:42 the density is significant. So then go, so this is a water
12:49 here at the water contact. We from high resistive ITty to low resistive
12:55 . And we go from low density high density. Okay, now,
12:59 do our velocities do? This is sonic log, This is sonic transit
13:04 , 100 to 200. Um 200 pretty, this is microseconds per
13:10 so this is not velocity, this one over velocity And 200 microseconds per
13:17 is pretty close to the velocity of . Okay, so we're in the
13:24 and we were fast, right, transit time is fast. We go
13:29 the top of the of the sand we said there was gas and the
13:34 are low and by the way they around all over the place, we
13:39 back into the sand and the velocities high again. So this is brown
13:44 and its velocity is pretty similar to shell. Now shales varying composition,
13:50 their velocities are varying, but the sand is not too much different from
13:56 shell. Now we go into this sand and this lower sand, we
14:02 have high resistive itty and we had density to the brian sand, except
14:08 the very top. It looks like have abnormally low density and if we
14:14 at the resistive Itty, it's slightly . So what's going on here is
14:20 a with ology changes it, a change. Um What's happening?
14:27 let's look at the sonic log and sonic log comes all the way back
14:31 the velocity of the gas. And the way, this bouncing around up
14:36 is called cycle skipping when you have in the drilling fluid that can attenuate
14:41 acoustic signals. So we we get lot of scattering. So the sonic
14:47 tend to be unreliable in gas but you can see kind of where
14:52 average is, and that's what we're here. So the interpretation is that
14:59 is a gas stand, but because resistance is low, because the gas
15:05 is low, and that's why the hasn't come all the way back to
15:10 it is over here. It's somewhere between. So this is what we
15:15 call fizz gas. It's low saturation . Probably not enough to be
15:22 but enough to affect your sonic So, this is one of the
15:28 of seismic direct hydrocarbon indication. You , the velocity drop, it doesn't
15:34 how much gas you have. A bit of gas drops, the
15:39 that means the a little bit of drops, the impedance. So a
15:44 bit of gas will give you a spot or other types of amplitude
15:50 So the so, and the kinds amplitude anomalies we were talking about
15:56 They don't really care how much gas there. They only care about the
16:02 or absence of gas. So they tell you if you have commercial saturation
16:07 not. But as we've seen, the gas lowers the modulation of the
16:18 . If it's a if it's a water mixture, it lowers the
16:24 And um but oil can also, the gas oil ratio is high
16:30 So here's an example of a bright caused by oil. This is an
16:36 reservoir, it's quite shallow. So fact that it might be, say
16:40 the module lists of brian was enough produce an anomalous amplitude. Here's another
16:48 of a bright spot due to This is an interesting case because you
16:54 a sand which is pinching out of and so down dip, You have
17:02 because you have a thick sand and the sand goes away the amplitude
17:07 So appear there's no sand down we have a thick sand. So
17:12 have a a gradual drop of amplitude you're coming up dip As the sand
17:18 pinching out but superimposed on that gradual . Suddenly here is a big amplitude
17:25 . That's an oil water contact. ? So this is an oil reservoir
17:31 the ship. Shell field 91 field the Gulf of Mexico. Alright,
17:40 if this were a homework assignment, would make you read Bachelor Alan Wong's
17:45 paper on fluid properties, but I'm gonna make you read it. Um
17:52 was gonna ask you to rewrite the . But instead, since we're here
17:57 , let's go over the conclusions of paper together. Okay, so number
18:06 , and this is really uh what would consider the most significant scientific conclusion
18:13 the paper and everything else is more less discussion. But here is the
18:20 . The primary seismic properties of poor which are density, bulk, modular
18:28 and the viscosity of the fluid. haven't discussed that. That's a little
18:33 more of an advanced topic. But and wong do in their paper and
18:38 properties vary substantially and they vary systematically temperature, pressure and composition. So
18:51 is the important conclusion from their And that's what we've been discussing in
18:56 section. The most abundant pour fluids brines. There's always water you you
19:06 never get 100% hydrocarbon saturation. So always some residual water in the formation
19:14 you could have gas, you could oil. If you're doing well,
19:19 analysis, you might have drilling fluid is permeated in the flush zone into
19:26 small analysts around the wellbore. We're worrying about that in this class.
19:32 we are worried about the bride the hydrocarbon effect and mixtures of the
19:38 . And so I've shown you how do all of that. A conclusion
19:44 the paper was that these enough attention in play placed on the temperature pressure
19:52 dependence of these properties. So in past, before this paper came
19:59 geophysicists would tend to oversimplify and go a handbook and read a value for
20:06 , a value for gas and usually S. T. P. As
20:11 temperature and pressure. So it's typically complicated than that, like as we've
20:18 , they say in particular, white can absorb large quantities of gas and
20:25 significantly reduces their modulates and density. as we saw before the gas oil
20:33 in an oil is a key So it's not just the api gravity
20:37 the oil, it's how much gas dissolved in the oil. That's a
20:42 a big swinger. And of course reduction can be sufficient to cause amplitude
20:50 , not just bright spots, amplitude of all kinds. Um So uh
20:58 the equations that battle and wang give you have a rough estimate of the
21:05 and a rough estimate of the institute and temperature, then you can calculate
21:11 their equations more realistic properties to use fluid substitution, which is our next
21:20 . Next we'll learn how we use oil properties to see how the velocity
21:27 Iraq changes with the hydrocarbons. so I showed you uh maybe I
21:35 show, you know, uh But an example of where we have a
21:41 cap on top of an oil So the top of the section has
21:48 in it and it's got oil under . So there's a gas oil contact
21:53 an oil water contact. And if gas happened to be in equilibrium with
21:59 oil uh where would you be on phase diagram? So another way to
22:05 that is at what temperature and pressure the gas be in equilibrium with the
22:11 ? And the answer is right there the with curves cross. So what
22:19 happen here at this? This pressure temperature would be the bubble point for
22:25 oil leg, but it would also the dew point for the gas
22:30 So you drop uh the pressure and the gas leg would want to precipitate
22:39 and the oil leg would wanna precipitate bubbles. So, an interesting
22:45 Of course those gas bubbles would gravity cause them to rise and form a
22:50 cap. Okay, so this one's you. Um you know, if
22:57 were homework assignments, I would have people go home and think about it
23:01 of giving the answer right off the . But here are some examples of
23:08 substitution and we'll learn how to do in the next section. But these
23:12 results from that fluid substitution. So start with different brian sands and we
23:21 a bride sand with 12,000 ft per . Another 1 10,000 ft per
23:26 Another 1 8000 ft per second. that's the velocity, that's what the
23:32 horizontal line is. That's our That's the velocity of the bride saturated
23:39 and then oil is added heavy Light oil drops it, the velocity
23:46 , lighter oil drops it more. here is gas, you know,
23:50 that's why I said, I mean oil, if you didn't know
23:54 You know, if you just picked number halfway, you know, if
23:57 picked this number here, I wouldn't too far wrong. Right halfway between
24:03 brian and the gas. But you know, there is some distinctive
24:09 on this graph. And so, of all, tell me what you
24:16 if you see differences in behavior, also explain the velocities, explain the
24:23 sand velocities and explain the change in with the hydrocarbons. So that's on
24:31 to chew on and to think And uh, I also welcome you
24:39 to, uh, to think about as well and whoever wants to explain
24:45 happening, let me know. I think I would say the the
24:56 the same rock sandstone, sandstone with velocity means it is have stronger
25:05 So it is less influenced by the in the pores and with more gas
25:18 the force velocity of the cubic will and the decrease. So let me
25:30 what you're saying here. You're saying I have a high velocity rock,
25:34 change with the gas from Bride to , that change is smaller than in
25:42 high porosity rock, because the high rock is more compressible, right?
25:51 why the velocity is lower. And why the change in velocity is
25:56 Is that? What is that? you meant meant to say.
26:01 so because I said it, I'll you're absolutely right. Yeah. So
26:09 see what's happening, uh the lower ferocity, the higher the velocity and
26:14 less compressible the rock frame is, the hydrocarbon effects are smaller. Of
26:21 , the higher gravity oil is less and more compressible than the lower gravity
26:28 gas is the most compressible. So has the lowest velocity and uh the
26:37 compressible rock has a smaller fluid effect the more compressible rock. Okay,
26:44 important conclusion. If there's one thing learn from this course, it should
26:49 , this summarizes a lot of what need to pull away from the
26:58 Okay, so thinking about a practical . Now, I have a brine
27:04 with a velocity of 6000 ft per . So that's this guy, which
27:10 so, say it started here and you could see that I would have
27:15 hydrocarbon effect that might be even bigger that. Right? So, if
27:20 have a brian sand with a velocity 6000 ft per second, Do you
27:25 why the sonic log might have difficulty the correct velocity of the gas
27:33 So the same rock skeleton as the sand fill it with gas. Do
27:40 see why the sonic log might have with that? Can you explain
27:52 Like one more time. Why? would be difficult. So,
27:56 I'm asking you to think about So let me, no,
28:00 I haven't. I haven't given you answer. I haven't discussed this.
28:06 when we uh you know, we won't get too well log editing.
28:12 if we got there, I would about the sonic logging tool and how
28:16 works. And it is a refraction . The p waves that the is
28:26 the velocity of our refracted waves along interface between their head waves, along
28:34 interface between the drilling fluid and the . I don't know if you remember
28:39 from Geophysics one but if the uh the formation has a lower velocity,
28:50 about if I have a high velocity , over a low velocity layer,
28:56 you're not going to get that. head wave developed. What you'll see
29:00 the direct arrival through the high velocity . So if the drilling fluid is
29:07 velocity than the formation, you're not to see a refracted headway from the
29:13 , you're going to see a direct through the fluid. So the velocity
29:17 would measure would be fluid velocity. ? So fluid velocity is around 5000
29:27 . That's approximately. I mean, varies with the type of drilling mud
29:30 everything, but it's in the vicinity 5000 ft per second. So if
29:35 brian sand has a velocity of 6000 per second, what would my gas
29:41 velocity be? Well here we saw change of over 1000 and the 6000
29:48 per second stand is going to be more compressible. Right? So this
29:53 more than 1000 for the 6000 ft second is going to drop more than
29:58 . That means its velocity is going be less than 5000 ft per
30:04 So if its velocity is less than ft/s, the Santa Claus can't read
30:11 as a matter of fact, I'll you an example of that when we
30:14 to the next section. So that's difficulty. The other difficulty of course
30:21 that if you've got a lot of in the borehole, you got gas
30:27 and you're propagating a wave through a mud with gas bubbles in it that
30:32 be highly attenuating. So you get skipping as we saw with the previous
30:39 . Okay, here we have an from a program that originated at
30:49 the company I worked for uh from Batt Cell there of the Battle and
30:55 equations Mike Batt Cell is the guy taught me how to do rock
31:00 Uh you know, I was a guy joined the Arco Research Center in
31:07 , took me under his wing. later went to be a professor at
31:10 colorado School of mines and he and han here at the University of Houston
31:16 great friends and ran a joint So actually this technology wound up being
31:23 a proprietary program that the University of has called flag and it is licensed
31:31 various oil companies and contractors, But when we were at Arco,
31:37 name of the program was fluid And what this program does is it
31:44 the battle and wang equations and you in the depth or the temperature and
31:50 . If you give it the it uses the geothermal gradient to calculate
31:55 temperature and pressure, um, you the oil gravity the gas oil ratio
32:03 the gas gravity that's dissolved in the . And it will input output the
32:09 of the oil. The uh, of the oil. So here it's
32:14 mega pascal's. All right. We've talking primarily about giga pascal's,
32:21 So 12 84 mega pascal's is 1.284 pascal's And there it is uh,
32:31 Giga Pascal's 1 1.2835. Uh, for the live oil with the dissolved
32:40 . Just for reference, the program tells you the dead oil module us
32:45 is without the dissolved gas in And you see here, it's
32:50 you know, 30% higher. One higher. Or yeah, about 1/3
32:57 . So, um, okay, with this program. This is for
33:04 properties of oil. But you could do it for the properties of gas
33:08 the properties of bribe. So here have live and dead oil density and
33:16 . And I would like you to go to the charts and at just
33:22 to read off the charts and that require visual interpolation on your part.
33:29 know at the same sort of temperature the same sort of pressure. Try
33:37 read similar properties for fresh water and and for pressure. Um two units
33:50 given to you uh p. i. Where we have our pressure
33:56 and P. S. I. if that's not what's on the chart
34:02 would have to do a units So I'm gonna ask you to go
34:07 that process and then show me the you come up with. And then
34:13 you know on a chart you would pressure on one axis temperature on the
34:19 axis plot live and dead oil Asus live and dead oil density.
34:28 two charts, one for modulates, for density, live and dead oil
34:34 and freshwater and saline water properties. there would be four points on each
34:41 . So do you understand the Do you understand the what you have
34:47 do? Know what charts? so last time I showed you modular
34:56 temperature at different pressures and I showed to you for oils. And I
35:02 showed it to you for brides and . And I also gave you
35:09 So you would have to go to charts there in your notes. So
35:13 you could pull them up on your and visually read values off of those
35:19 . So I'll do it here. there there's a module asse. And
35:32 the units of pressure are in bars . I think they changed the units
35:37 their paper but in the figures I , they are in bars so it
35:42 um the the fluid vell output. , so basically visually if they give
35:51 a pressure, you know, interpolate in between at the temperature and the
35:58 and read the value of for module and do it for fresh water.
36:04 see that's this guy and do it saline water. That's this guy.
36:12 read off the module is do the thing uh with the density, do
36:19 same thing with the density and make chart with four points on it.
36:24 modular and a chart for density. see what I'm asking? Yes.
36:33 , so I'll come back to the and so just proceed. And when
36:45 ready to let me know when you're to have me look at um what
36:50 what you've done. Okay for that module asse? The freshwater was zero
37:35 the brian was 300,000. Yes. . That's parts per million of sodium
37:44 ions. Okay. Okay let's see I can do. Yeah, I
45:27 I got for values. I'm gonna sharing. You show your share your
45:38 . Okay. Oh sorry that was end of that section. So I'm
45:47 close that file and we want to , well where is it? I
46:02 I had it. Excuse me, open. We're gonna have to.
46:20 it is. Okay. So the order of business and I apologize,
46:35 slide could be misleading. That's not borehole, right? This is a
46:39 of the earth with a brine And this is the same piece of
46:44 where some of the brine has been out and has been replaced with
46:49 So this is what we call fluid . And the velocity of the bride
46:56 in this case is 8000 ft per . As an associated shear wave velocity
47:02 associated density we add gas. What the p wave velocity comes down,
47:10 shear wave velocity increases because the sheer doesn't care about the fluid module
47:17 But the density is lower when you gas. So the shear wave velocity
47:22 increases a little bit and the density down because it's a porous rock and
47:29 gas is lighter than the brine it . So that's what happens now,
47:38 wanna be able to calculate that So we want to go through the
47:43 to do this and by the way is from The work done in the
47:52 60s by Mike Forrest, who was guy who discovered bright spots and um
48:02 interesting because he has shale and bride velocities that are around 6700 ft per
48:11 on a sonic log And he's got gas and velocities of 5000 ft/s.
48:21 , remember what I said about the log measurement chances are these gas and
48:27 were even lower, but the sonic couldn't read it, but you
48:32 it wasn't so wrong that it didn't him understand that the gas sand should
48:36 much lower impedance than the bride sand by the way, we do have
48:41 right there are contacts here. Um you have sand either filled with gas
48:50 filled with brian. You see when filled with gas of a very low
48:54 , when it's filled with brian, have a higher velocity. So,
48:59 this gave him the idea that, , the gas sand will then have
49:05 lower impedance than the brian sand. where I have a gas reservoir,
49:11 should have a stronger reflection coefficient of the shell and the gas sand.
49:18 shell gas sand reflection coefficient, it's big change in velocity with density,
49:25 shell to brian sand is a smaller in velocity and density. So you
49:32 have a higher reflection amplitude from the sent. And of course we've seen
49:41 in the laboratory as well. So we have the velocity of a sand
49:47 happens to be a sandstone from offshore in the south china sea. And
49:55 had the compression of velocities uh for dry rock or here they say gas
50:03 . So probably they really mean air . And you have the shear wave
50:10 for the dry rock or I should the gas saturated rock. So now
50:17 is versus pressure. They don't tell what type of pressure. It's either
50:21 confining pressure or differential pressure. But the velocities are increasing with pressure,
50:28 can assume that the differential pressure is . So um you uh fill these
50:38 measurements not calculations, you fill the with brine and the velocities increase and
50:46 increase more at low pressure than they at high pressure. Why is
50:54 Why do the velocities increase more at pressure than at high pressure? The
51:04 space? Yes, the low, , the low low pressure, the
51:11 is lower velocity. It's more Right? And so maybe the ferocity
51:16 a little bit higher. Which you see here on the chair wave will
51:20 to that next. The porosity is , but also the flatter pores are
51:25 open. Right? So as you the velocity, the velocities, I
51:30 as you increase the pressure, the increase, but the change in velocity
51:37 to the fluids decreases. Alright for the sheer wave things go the
51:42 way you add water and the shear velocity goes down. Uh Why
51:58 You add water? You increase the . The sheer module is doesn't
52:03 you increase the density and the velocity down and in high pressure, the
52:10 is less, so the density goes less. So you get less of
52:14 change. Okay, so We are to use uh equations that the industry
52:27 been using for the past 70 And these are called gas men's
52:34 And what gas mains equations do is calculate the bulk module asse of the
52:43 rock with whatever poor fluid you have bulk modules of the bulk rock and
52:52 a function of the porosity of the . The fluid module asse the modular
53:01 the solid material and the modular of skeleton without the fluids in it,
53:09 call this the dry modulates that in application is actually a misnomer because the
53:18 isn't dry in the laboratory, it be dry, but in the earth
53:22 not dry. So I prefer to frame module asse or skeleton modules.
53:30 most papers refer to it as the modulates. So what gas mains equations
53:37 is they express the bulk modulates of saturated rock as a function of these
53:48 . And then of course you get velocities, you have to know the
53:53 modular. Um But if you have sheer module asse you could calculate the
53:59 module asse of the rock. Maybe had a brine saturated rock and I'm
54:05 add gas. So I calculate from equation. The change in the effect
54:11 module asse and the sheer modulates stays same and I use mass balance to
54:18 the change in density. So I calculate how velocity changes from an initial
54:24 Gas mains equations don't make the rock its components. It takes the rock
54:32 under one condition and tells you what velocities are gonna be when you're saturated
54:38 another condition. And there are a of assumptions in gas mains equations.
54:45 one thing, gas men's equations only uh perfectly well, not even
54:53 There are only supposed to be applicable chemically homogeneous rocks. So one
55:02 so a pure court sandstone. In , we use various tricks to take
55:09 account mixed little ology is with a of minerals and we'll talk about how
55:17 might do that. Uh They also the rock is Aissa tropic and of
55:24 everything is linear. We have small , This is a deviate oryx
55:29 As the wave passes through the it compresses and cheers the rock a
55:35 amount. And so uh the rock itself is an elastic medium. The
55:46 frame with fluids in it is what call a poor elastic medium. It's
55:52 perfectly elastic because it has fluid solid . So it has attenuation. We
55:59 treated as a visco elastic medium. , so how do we do fluid
56:09 of the density? Well, this our old friend, we have the
56:14 which is the poor volume divided by total volume. And we know how
56:20 density is related to porosity. And from the mass balance equation where we
56:27 these volume fraction of solid material times density of the solid material. And
56:34 log analysis, they call that the plus the volume fraction of of
56:42 which is the porosity times the density the fluid. Now if you have
56:47 mixture of fluids you use mass balance to calculate the density of the fluid
56:54 and if you have a mixture of again you have to do the same
56:58 , You have to use a volume average of the densities of the
57:04 Okay, that's the easy part. The hard part is gonna be when
57:12 uh add the fluid. So the thing we need to do is we
57:16 to know the module asse of the . Right, So we have the
57:21 among equations which give us the ma of the pure fluids. And if
57:26 have a fluid mixture, we use equation to calculate the module asse of
57:32 fluid mixture. And of course the of the fluid mixture again comes from
57:37 mass balance equation. Now Woods equation supposed to be applicable. If we
57:45 a homogeneous distribution of fluids um it a Royce bound, it is a
57:54 bound. So if we if we a different distribution of fluids uh say
58:01 pores have different saturation in them then would have something higher than the Royce
58:09 . And so the highest possible fluid , we could have would be a
58:14 bound of the fluid modules. And would be given by this equation.
58:19 there are situations where that seems to more applicable. I don't know if
58:25 get to talk about that, but our purposes we're assuming homogeneous saturation and
58:31 operating at near zero frequency. so now we're gonna assume a few
58:42 things. We have a rock We have a poor space filled with
58:50 and we want to combine these properties calculate the properties of the saturated
58:56 This is these are called gas mains there, it's sometimes called B.
59:01 . Gasman Theory because it's the low limit. In fact, zero frequency
59:07 of BeOS equations or was supposed to . It turns out very recently,
59:13 very own leon Thompson, who, the way, is the most cited
59:19 in our society journal Geophysics. So most sided geophysicist in exploration geophysics,
59:27 come out and he's proven that gas equations are in fact wrong. They're
59:35 the low frequency limit of the O equations. BeOS equations are
59:40 Gas mains equations have an error associated them. And these are the equations
59:45 been using and I'm going to show how to use these equations keep in
59:50 that one thing my students and I leon Thompson are working on our how
59:56 do fluid substitution correctly. So, mean, gas mains equations can't be
60:03 wrong because uh the industry would have that the predictions are bad,
60:11 So the results are in the right . And so they're close enough to
60:17 right answer that people didn't notice any problem with using them, but in
60:25 they're slightly wrong. And so uh are better ways to do fluid
60:33 but I think that's beyond the scope this course and by the way,
60:36 much harder to do correctly. So gonna stick with gas mains equations.
60:44 so some assumptions have to be The rock is ice a tropic and
60:51 . Uh the sheer module asses not by the fluid. So the skeleton
60:57 independent of the fluid. So the this is a purely mechanical effect.
61:02 are no chemical reactions between the fluids the solids. So and so the
61:09 material is chemically inner. Uh the fluid is firmly coupled to the
61:17 We have small stresses. So there's turbulence turbulence of the fluid as it
61:22 around. There's there's no there's no . You don't get open space.
61:28 fluid is is always filling the entire space. And uh probably the most
61:37 assumption is that the poor pressure is equipped vibrated throughout the rock. That
61:45 that every one of these pores, pore pressure is the same. And
61:49 could see that, that would not the case if the rocks, if
61:54 if the pores were not in communication each other. And and the rock
62:00 enough, that fluid can move freely the pores. Because obviously, if
62:04 have a very compressible pore, or have an in compressible spherical poor,
62:10 I apply a given stress to the , the fluid in the compressible pore
62:16 going to be more compressed, it's molecules are going to be pushed closer
62:22 and their fluid pressure is going to higher than the fluid in the spherical
62:29 . So that's an assumption the rock permissible enough that the fluid pressure equally
62:37 . And by the way there there's it may take time to equip vibrate
62:42 all the pores. So it means got to be a low frequency
62:48 If you are in very high there wouldn't be time for a quick
62:53 . So, lots of assumptions to at a wrong equation, but that's
62:58 we are. And so, uh way it works is given the bulk
63:06 and densities of the fluids and the modules and density of the solid
63:13 Remember, it's at least conceptually it's single solid material, we're gonna treat
63:19 like a pure mineralogy. And by way it's also wrong for that
63:24 Uh The way we make corrections for multiple minerals is not exactly right
63:30 So that's another degree of being Uh And we're also given the bulk
63:37 list and density of the rock at known saturation. And so what we're
63:44 gonna do is gonna change, we change the modulates of the fluid,
63:48 why might that happen? It could due to a temperature or pressure
63:52 or it could be due to a change, or it could be just
63:58 different fluids. So, um, know, a typical application would be
64:04 have a water sand And let me substitute and put southern gas, maybe
64:12 gas saturation into that water sand. does the p wave velocity of the
64:19 change? So, uh so that the problem. So, before we
64:27 get into dealing with the equations, time for our early break. So
64:33 reconvene will take approximately 10 minute We'll reconvene at 20 minutes after
64:46 Okay, let's go to gas men's . So this is it. And
64:57 I do have to warn you that notation changes throughout the course, because
65:01 took slides from various people, but really good for you to have to
65:06 to deal with different notations. I'm doing you a favor by being
65:12 and not making the notation uniform throughout class. Right, You're just gonna
65:17 to adjust every time you look in , you're gonna have to think about
65:22 the notation is. So this is men's equations expressed in terms of
65:29 So the velocity squared is equal to module is here divided by the
65:37 Right? So there's the density. what is the modulates of the
65:43 Well, it's K plus four thirds but mu doesn't change with the
65:49 So it's a constant there. The skeleton itself, you could think of
65:55 plus four thirds mu as being the of the rock frame. The rock
66:02 . The dry rock. So KB the dry rock bulk module asse.
66:09 is the dry rock steer modulates which the same irrespective of the fluid
66:15 So that doesn't change. So then this term this guy which shows the
66:25 of the fluid or calculates the effect the fluid. And so there are
66:30 important parameters. Here, one is dry rock module is divided by the
66:38 solid grain bulk module asse. So K dry over K solid. That's
66:48 that you need those parameters. You the porosity and you need the fluid
66:54 . So the change in p wave with the change in fluid module asse
67:00 all due to this guy. there's a little bit due to the
67:05 in density, but if all I'm is the fluid module asse, that's
67:09 it happens. So essentially it adds turn to the module asse of the
67:15 . And you could think of this changing the bulk modulates of the
67:24 Okay, so you're saying saying this different terminology, this is more typical
67:33 now? Instead of V P I pulled density from the other
67:38 So this is roe V p squared that's what's that? That's the plane
67:43 modulates to the rock. That's Alright, so this is M.
67:48 is K plus four thirds view for rock. Well, there's four thirds
67:53 and it doesn't matter what the fluid is. So K of the rock
67:57 equal to K Dry plus this term we saw before. It's got the
68:04 of K dry two K solid. got porosity in it and it's got
68:11 fluid watch. Allison it now. what is this? One? One
68:26 K. Dry over K of the . And you see it here,
68:32 minus K. Dry over the bulk of the solid. That's called the
68:38 O coefficient. And what that thing is the change in poor volume divided
68:46 the change in volume of Iraq. for the dry rock. And that's
68:55 to the porosity times the bulk modulates the dry rock divided by the bulk
69:02 of the pore space. So that's compressible the pore spaces which is one
69:09 K. Dry over K zero. you can express gas mons equation.
69:15 way the bulk modulates of the saturated is equal to K dry plus the
69:23 coefficient squared times M. Which is by this equation here? So this
69:39 , oh coefficient, when ferocity is , what is the B O coefficient
69:45 to be equal to? Well, porosity is zero uh K dry is
69:52 to k solid. Right? There's porosity, there's no poor space.
69:58 that's one. So the bl coefficient zero. What happens when porosity is
70:06 to 1? Well, when porosity equal to 1? Uh uh there
70:14 no skeleton module, asse soak a must be equal to zero. So
70:21 Bo coefficient is one. So the of the bl coefficient is 0-1 and
70:30 how it varies depends on the the K dr K matrix. Uh Now
70:45 zero, you could say is high , low consolidated uh material, uh
70:53 sediments would k dry would be very . So the B. O coefficient
71:00 be closer to one. Okay, now let's take a typical rock in
71:09 gulf of Mexico, a typical sandstone . And we start with the brine
71:15 velocity. We add gas from 0% , I mean 100% gas to 0%
71:25 here and we change the fluid module according to woods equation. And what
71:33 find is, you know, basically by Woods equation. Woods equation is
71:38 on off switch. So a compressible , the velocity is also an on
71:44 switch. A little bit of gas you the maximum change in velocity and
71:50 you get a rebound, it comes and that's because as you keep adding
71:55 , the density decreases. The module doesn't change much. So this is
72:05 same plot, but also showing what to the shear wave velocity. And
72:10 see the shear wave velocity is varying the density. So the shear wave
72:15 is increasing all along linearly. As add gas, p wave velocity drops
72:22 then it increases along with the shear velocity. So you can see out
72:27 , the V. P. V ratio becomes constant basically, you're canceling
72:32 the density effect. Okay, so an example of doing it. Uh
72:46 this fluid substitution on real rocks in earth. So you have a nice
72:53 here and here. Here is a sand, yellow is the percentage of
72:59 , gray is the percentage of courts . The percentage of water And uh
73:07 is the percentage of gas. you see there's more gas than water
73:12 . So we have a gas saturation maybe 70%. and so this these
73:19 the NC two values. Right? , uh the uh the density
73:32 the red curve Is the original measured in c. two. And the
73:40 curve is in this sand. Take the gas and make it all
73:48 And so that's the velocity you I noticed the effect on the shear
73:54 velocity is very small, but it in the other direction. The fluid
74:02 was only done here because this, water saturation is calculated to be all
74:08 . There was no gas down Alright, so the gas gas effect
74:17 often an on off switch light the velocity will decrease as you add
74:24 oil, but it will be a linear thing because it's module asses closer
74:28 the module asse of brian. If start dissolving gas and the light
74:34 it can start acting more like You could actually increase the velocity with
74:40 oils because they're modulates could be more more than the brine. That would
74:45 a very, very heavy oil and don't encounter those very often unless you're
74:54 the, you know, uh either highly bio degraded where you get a
75:00 mat, for example, it's practically or it could be uh in arctic
75:06 or antarctic areas where um the temperature low and the oil is almost
75:13 Then you could get velocity increases where have oil. Now, there are
75:22 different ways to express gas mains Uh This is the way he expressed
75:29 in his original paper, where the bulk module asse is equal to the
75:39 module asse times this ratio. And ratio has this factor que in here
75:47 Q depends on the fluid modulates the . The frame modular and also remember
75:55 sheer modules doesn't change. So this the way gasman wrote it in his
76:00 paper, this is a more conceptual to write gas mains equations And sometimes
76:10 helpful thinking of it this way it's helpful for computation because you're not solving
76:16 for case, sad you're solving for ratio here. But the symmetry of
76:22 one is nice. It's interesting. right, so uh You have the
76:29 for the saturated rock and K0 is solid rock is equal to that ratio
76:36 the dry rock plus that ratio for fluid. But there's this extra term
76:45 porosity here, of course, the ferocity you have, uh the more
76:53 want that fluid term to be Um We'll come back and we'll actually
77:01 this form later on, it's a convenient way of writing gas mains
77:10 Now, one of the parameters you to do fluid substitution. Well,
77:16 one way to do fluid substitution is solve for the dry modulates given the
77:25 of the saturated rock. So if had VPN B s with V P
77:31 p B. S in density. with roe V P squared, I
77:35 get K plus four thirds mu and roe V s squared I could get
77:42 . That gives me a K. the saturated rock, I can now
77:49 for the dry modulates and so I K. Now s is not
77:56 it's the saturated rock and I have , I have fluid module asse and
78:02 have the modulation of the solid So uh there we uh uh can
78:11 we have K. D. Now could change the fluids but to do
78:15 I need to have the shear wave . Okay so uh just taking you
78:25 some typical workflows for how we do . So I have K for the
78:32 rock. So that's the saturated rock equal to K. For the dry
78:41 plus one minus KD over K. squared divided by one minus porosity minus
78:50 over Ks divided by K. Solid ferocity divided by K fluid. And
78:57 have the sheer module I equal. I need to get each of these
79:02 . I need to get K I need to get get K.
79:06 . K. Matrix. Well Matrix I calculate from the composition if
79:13 pure courts, I know the uh module. List of courts. So
79:20 could I could look that up in in a handbook if it's a mixture
79:25 minerals. We use the bounding equations we take the Royce, void bounds
79:31 the different minerals. Typically we average that's called the hill average. We
79:37 the average of the Royce and void . So that gives me the matrix
79:43 asse, fluid modulates. I used Bachelor long equations porosity comes from log
79:50 . Uh K. D. Will have had to have solved for
79:54 other way. And so we could V. P. M.
79:59 S to do that but if we have B. S. What would
80:02 do? Well we could use trend and I'll show you how we do
80:10 . Um So we start with both of the 100% saturated rock. We
80:20 by, Well this is if we're with 100% saturated rock, we multiply
80:29 uh The density of 100% saturated The times V. P squared minus
80:37 thirds V. S squared. So gives me the bulk module asse of
80:42 100% Brian Saturated Rock. And the modulates of the 100% brian saturated rock
80:49 the density times B. S Okay, now I'm going to calculate
80:58 dry frame module asse from the matrix asse using this expression here where these
81:11 the terms for those expressions? So I have an algebraic equation which
81:18 me to calculate the dry frame modules these values. Right? So I
81:29 the bulk modules of the 100% saturated . The bulk modules of solid,
81:35 could get X and Y. I plug plug X. And Y.
81:38 here. I get the dry frame . Now I'm ready to change the
81:43 module asse and do my fluid I had so to do fluid
81:51 I have two fluid substitute the density the way. Here's a four trip
82:01 um historical purposes. Here's a four subroutine to do this and it's like
82:08 lines of code. That's all it . So it's pretty easy to do
82:12 I start with 100% brian saturation. , so um yeah, with
82:20 with the uh dry frame module once I get this, then I
82:26 go back to here and I could my fluid substitution. I can see
82:31 the bulk modulates of the saturated rock with the bulk modulates of the
82:40 Now there's a complication in that. assuming that the fluid is homogeneous,
82:50 every pore has the same fluid same saturation of gas or oil.
83:03 This is an interesting way of plotting here is instead of velocity is
83:11 Right? And so where velocity where saw the rebound, do the
83:15 right. The velocity came back as add a gas. Of course the
83:20 continues to drop because now you're multiplying density for velocity, you're dividing by
83:26 square root of density. So it back, but now you're multiplying by
83:31 bigger number. So it goes down by the square of the density.
83:37 dividing, you're decreasing the density and so velocity comes up by the square
83:45 of density, but impedance goes down with density. You're multiplying by the
83:52 . So this is our fluid saturation . Uh Now, if you don't
83:59 a homogeneous distribution of fluids, you something called a patchy distribution and there
84:08 all kinds of variations on this. all there are many different ways that
84:13 fluid may not be uniformly distributed, if it happens to arrange itself in
84:21 certain way, you may wind up a more linear dependence on fluid
84:32 which brings us to the patchy saturation . And in many ways this is
84:38 of an upper limit on what the could be. And uh the reason
84:45 this is if the if I have mixture of materials with the same share
84:53 asse, then the plane wave modulates reciprocal of the plane wave module,
85:01 uh is equal to the volume weighted of the reciprocal of the different module
85:07 So in a way it's it's it's to a Royce bound for the different
85:14 . So, if I could have patch filled with gas, a patch
85:17 with oil patch filled with brian, sheer modulates is not supposed to be
85:23 , right? So therefore this equation exact. Now, of course,
85:30 begs the question. Why are you with different fluids? If if the
85:35 is exactly the same, Such that show module, this is the
85:39 Why do you have different fluids? , the patchy model doesn't necessarily reproduce
85:46 accurately the behavior, but it it of gives us an upper bound for
85:52 the module is. Could be So now let's take a rock and
86:02 uh substitute different fluids in the rock let's bury the pressure. So we're
86:11 the modulates of the rock, we're going to let the porosity change too
86:16 . So most of the dependence on here, this is a carbonate.
86:21 of the dependence on depth is due closing of low aspect ratio poor.
86:27 the effect on the total porosity isn't . And we have the water saturated
86:34 that might have come from laboratory measurements pressure was a proxy for depth.
86:41 we have a water saturated trend. put a very heavy oil in and
86:46 can see at low pressures in low shallow, there's a certain geothermal
86:53 assume the heavy oil is faster than water deeper. The heavy oil is
87:00 than the water because the temperature effect going to take over, it's
87:05 it's stronger on the heavy oil. is a dead oil. What is
87:10 dead oil? It's an oil where no gas in solution. Uh,
87:17 you don't keep the oil under if you release the pressure, all
87:22 gas will come out because you've dropped the bubble point. So that is
87:28 the dead oil. It's well It's not volatile. It doesn't have
87:35 bubbling out of it anymore. The is all gone. So this is
87:40 dead oil and it's more similar to . But again, as you get
87:46 , the difference gets greater because the of temperature is more, this is
87:51 light live oil. So the gas never allowed to come out of
87:57 it's velocities are even lower. And course gasses even lower. So if
88:04 didn't know the properties of the if you had to make a
88:07 you know, somewhere in between water gas, maybe halfway in between.
88:13 as you get to very high you're getting more and more like
88:22 Okay, Now, let's look at happens when we measure velocity versus saturation
88:28 the laboratory. And these are gas equations, which by the way,
88:34 told you were wrong, right, people thought they were right. And
88:41 we've seen is a big discrepancy in laboratory, especially at low gas
88:48 So, the dash line is what predicts the black line and the points
88:54 what are measured in the laboratory, a big difference and even a difference
89:00 the shear wave velocity. So, happening and a big part of what's
89:09 is the gas is not uniformly Also, remember, in the
89:15 gas mains equations are the low frequency . We have to take into account
89:20 fact that laboratory measurements are very, high frequency, they might be at
89:25 megahertz. So, uh we have do something better. Alright,
89:34 coming back to gas men's equation um this way, what happens as we
89:45 the pore fluid. Right? I as I changed the fluid module
89:52 say, I have two different fluid . I I could write this equation
89:56 , couldn't I? I could write for fluid modulates one which gives me
90:02 modulates one. And I could write for fluid module is two, which
90:07 me saturated module is to I could the equation twice and then I could
90:16 the equations from each other. And is what I get right. I
90:24 a change. This is this is . D. Over K zero
90:33 D. For fluid saturation one. this is the same quantity K.
90:40 it's not supposed to depend on the from saturation state to and fluid
90:50 So, you see, I canceled the dry frame modular snap.
90:57 isn't that interesting? Um But I've telling you all along that fluid substitution
91:04 on the dry frame module asse. I do fluid substitution right here,
91:10 could cancel out the dry frame So where is it? Where is
91:18 dry frame modular? Do you believe that the fluid? I've been telling
91:34 over and over again that the fluid is bigger when the dry frame module
91:40 small. Alright, haven't I been you that? Am I a
91:45 I just proved. Didn't I just that wrong? I don't see the
91:50 frame module is here. Doesn't this that the dry frame module is the
91:56 substitution doesn't depend on the dry frame . I think it Maybe inside the
92:08 . zero. Well it's not inside . Zero but it's inside K.
92:13 . And K. Uh K. . One and K. S
92:16 So the answer is it's not explicitly , but it's implicitly there.
92:24 It's implicitly in these module I so but I could do I I don't
92:31 to solve for the dry frame Right? I could I could do
92:36 substitution right here. Right. If have K. S. One and
92:41 F one, I could then solve K. S. two.
92:47 I change I changed the fluid So this is known. This is
92:53 . This is known. I could the new state. Yes.
92:59 So I don't explicitly have to calculate dry frame modules, which is
93:07 Okay, so previously showed you a , laboratory measurements where uh the
93:17 the goal of mine, we have velocity versus depth of the stolen mine
93:22 on laboratory measurements and equivalent pressures. I think I told you that laboratory
93:28 tend to overestimate the effect of pressure of damage to the core.
93:38 This is more typical. And these come from velocity versus depth. Friends
93:45 logs. So, uh, if look at velocity versus death from logs
93:52 in sand stones. Uh, this in the gulf coast. It doesn't
93:57 that curvature to it. It's a linear relationship. So, I could
94:03 fluid substitution on that guy. I put a heavy oil in and
94:08 very shallow. It might actually be . Uh, I put a light
94:14 oil in and shallow. It's kind halfway in between deep. It becomes
94:19 similar to gas And here we have gas effect there. Again, the
94:26 effect is much bigger, shallow than is deep. Okay, so here
94:35 some laboratory measurements. Um The dash is gas mains equation is the prediction
94:43 Gassman from the dry VPs. look at these observations and hypothesize the
94:55 for the for the observations by the , where you have two measurements at
95:01 same pressure. That's a history one measurement is pressuring up, the
95:10 measurement is pressuring back down. So showing you the effect of history.
95:16 on these measurements. Okay, now what's going on here with the saturated
95:25 not Well, just, just explain the velocities. Why is the velocity
95:31 what it is? I mean, kind of it matches the earlier one
95:47 we were looking at for the sandstone china similar. So it's just as
95:53 pressure increases, its more compressible at lower pressures and creases. That's that's
96:03 velocity. Look at your wave Do you see something funny about
96:12 I don't know it's switched. What's happened. What's happened is that's
96:33 weird, Dad is completely opposite with other one. So, what happened
96:45 , well, think of the equation the for shear wave velocity. We
96:52 . If the only thing that's changing density. The saturated rock should be
96:58 , but it's not just slower. faster. What does that mean?
97:05 means that the rigidity has increased for saturated rock. I've changed the rock
97:14 the effect is bigger than the history effect here. You see the history
97:19 effects. Right? So, probably mike battle was worried that history says
97:26 the explanation. That's not the This is because the rock has a
97:34 has a greater share modulates when when than when dry. Is that
97:42 Yeah, it's called frame hardening. gas means equations assume no chemical
97:51 but especially when you have clays, have the habit of swelling and interacting
97:57 fluids. So Claes can cause the to harden. Uh They could also
98:07 this frame to soften. Its it's complicated situation. Sometimes water hardens the
98:14 . Sometimes it softens the frame. that's why you shouldn't use the dry
98:20 skeleton. Uh Or you shouldn't use dry rock module. Is to predict
98:26 saturated rock module. Asse you should the inverted frame module asse from uh
98:34 all the equations measuring be PBS density for the frame module asse. That
98:42 the module is that should be used . The module is measured on the
98:46 rock. You want the module asse the rock frame in the presence of
98:55 poor fluids that are present in Two important lesson. Okay, now
99:07 a really good paper in geophysics that pointed out before TED Smith? It's
99:12 2003. These were some slides I from him in 2006. And he
99:19 he works through uh the fluid substitution problem. And the reason we're going
99:27 all this is because I'm gonna ask to do this, I'm gonna ask
99:30 to code up all of these equations produce a result. So um first
99:41 you need V. P. And . S. V. S could
99:45 measured or it could come from one our V. P. B.
99:48 . Relationships that we know so Right? So we get the bulk
99:54 of the saturated rock under the C. Two conditions for using log
100:01 and log B. S. And using here, G. For sheer
100:06 . Usually we use mu he uses . So you calculate those next.
100:13 calculate the dry frame module asse. he uses this equation. I showed
100:19 an equivalent way to get there I had the X. And the
100:23 . And kind of simplified things. I was following a procedure outlined by
100:31 in his review paper. But his case star is the frame module
100:39 . I don't like to call it dry modulates the frame module asse.
100:44 , once you have the frame module you could calculate the saturated module is
100:49 new conditions. So you change the module asse. And uh Let's
100:57 I'm trying to look at his equation . Yeah, this K0 is his
101:02 module asse. And yeah, this it's this is another way of writing
101:09 mains equation. This is correct. um that's your new saturated modulates with
101:20 your new pore fluid is. Uh also have to do fluid substitution on
101:26 bulk density and then you calculate the velocities with the new saturated module asse
101:33 the new density. Okay, that's workflow, I'll take it through through
101:43 . I'll work the problem a little way. I'm saying, given uh
101:49 ferocity at 100% water saturation, Compute . P at water saturation of
101:58 So this is the equation I need solve, I need to know the
102:01 module is at 50%. The share is at 50% saturation and the density
102:08 50% saturation. Okay, so I to go about getting these things.
102:16 , so uh first of all, either have measured B. S.
102:22 I have V. P. And trend curve. And I could get
102:26 And from that roe v A squared get the share modulates at 100%.
102:34 that gives me the share modular at . Um If I only have ferocity
102:41 I have to compute the density. I can use mass balance to do
102:46 . And so given the density and shear wave velocity, I get the
102:50 module is at 100% saturation. Uh I set that equal to the sheer
102:56 at 50% saturation. We're assuming we're c. two. We haven't dried
103:02 rock, we haven't changed the rock and still in the presence of the
103:06 fluids if it was water wet before water wet now. So I keep
103:12 share module is the same. I have two fluid fluid substitute the
103:19 too. So I use a new density. Right? So I used
103:24 water saturation and the densities of the , the density of the water.
103:30 I calculate the new uh the new of the 50% saturated rock.
103:39 now I need the bulk modules of saturation. Well, here I have
103:44 well known gas mains equations. Got dry module list. Um And the
103:51 modulates which I had to come get someplace, maybe one of my papers
103:57 a handbook, someplace the fluid modulates Battle and Mom. Um Well from
104:04 based on battle and Wong's equations for for the different fluids. Um So
104:13 can solve um we gave you the to solve explicitly for K. 50%
104:20 you had uh you know uh from . P. V. S.
104:27 100%. I'm sorry to solve for . Dry if you had be PBS
104:33 density, you can solve for Dry if you're in a sandstone,
104:38 an easy relation that K dry is to the share module asse. It
104:44 coincidentally turns out that way. So could do it that way or you
104:48 be more precise about it and explicitly K dry using the equation that I
104:55 you. Okay then we have K and we have K oil and gas
105:00 the water from the bats, Lynn equations and we have water saturation.
105:08 so we calculate the new fluid module this is woods equation. Okay,
105:14 that's the prestige. So you will that in exercises but we're at the
105:19 of the hour again. So let's at 3:11. Okay, okay.
105:32 as I said, we have different , We have this approximation uh which
105:39 given by that equation. All you is brian sand velocity to calculate
105:45 sand. And we have the math approximation where you use em instead of
105:52 and you could get em from roe p squared. So that's nice.
105:59 we compared to the exact jasmine's equations different ferocity ease. And what we
106:06 is uh if we look at the For uh ferocity is greater than
106:14 Math cause error was bigger than ours it could approach 100 for very porous
106:24 . The results were similar For non rocks below 10 Moscow's approximation is better
106:34 my empirical equation. Uh but they're terrible. Okay. And fluid substitution
106:42 10% ferocity is imprecise anyway because your error introduces a big error in your
106:53 . So, you know, I say my approximation is pretty good
107:02 we'll come back later and and we'll to look at the aero sensitivity of
107:08 men's equations. All right now, I said where where the fluid module
107:14 is very low, like a low . Uh your fluid substitution is an
107:21 off switch. And here dr Bassel battle and han in the newspaper,
107:28 plotting impedance versus saturation. P wave peter and shear wave and peters and
107:34 resulting poison's ratio. and uh here only 10% gas saturation, uh you've
107:43 all the change in velocity in impedance gonna get. And then after that
107:48 it's a pretty mild change. So again, on off switch,
107:55 but at high poor pressures, that becomes more gradual because the gas modular
108:05 much higher because of the higher poor . Okay, now, um we're
108:16 look at inferences that we could make gas men's equations and we could do
108:25 like cross plot frame module asse versus modular in a sandstone. So in
108:34 sandstone, um we know the poison's of the frame is about 0.1.
108:41 if we know the frame module we know the sheer modules. Remember
108:45 modular sequel, sheer module asse When poison's ratio is close to 0.1 or
108:53 module is approximately equal to share So uh I could just vary the
108:59 module asse and I could calculate the modules for a given fluid saturation four
109:09 of constant ferocity, that's the that's the other unknown. So I'm
109:13 a sandstone. So I know the bulk module asse. I'm good at
109:20 a range of ferocity ease and each is going to take on make a
109:25 curve and then I'm going to vary frame modulates at that ferocity. And
109:30 I'm going to calculate the satch, the saturated module is giving the fluid
109:35 asse. And this plot is really . And you could make all kinds
109:41 inferences from this. Uh For I could, you know, if
109:47 take take porosity zero then the saturated asses equal to 38. Right,
109:56 right. It's equal to the solid . So, whatever it was
110:00 uh that uh doesn't change, but I could theoretically At a very low
110:12 here. This curve is for 1% . I could theoretically produce a very
110:19 frame module asse if I had very flat cracks. So, a
110:25 like this, although not you won't that in practice. In theory,
110:31 curve is is physical. It's it's realizable, right? It doesn't it
110:38 happen for other reasons, natural but mathematically it doesn't violate any
110:45 Mathematically, it's legal to have that . Um And I can compute the
110:54 curve for 5%, porosity, 10% . And then look what happens is
111:01 get up above 20% porosity. These converge, This is 40% porosity and
111:14 going to get really, really wild go all the way to a ferocity
111:19 one. So I'm approaching one As I approach one, I would
111:27 this line, this is a lower on what the saturated modulates could be
111:35 a given frame modulates and we could some inferences here, we could
111:45 wow how if I get a if I have a saturated modulates up
111:51 and a frame module is down That could only be created with low
111:57 ratio pores. And it also tells that rocks naturally occurring rocks like in
112:06 gulf of Mexico porous rocks are gonna a very similar relationship between saturated modulates
112:14 frame modules. That's why we could away with an empirical equation between Vp
112:22 and vP gas. But this is get wilder, This is saturated module
112:31 versus freight module asse, I could this to VP VS. B.
112:37 . Right? Because remember I said sheer module asse is um is equal
112:45 the frame module us in a pure . So, for a pure
112:51 if I know the frame modulates, also know the sheer module list.
112:55 I know V. P. And . S. Given a density
113:02 Right? So now I could produce same kind of plot. So I
113:08 Vp VS. B. S. of saturated modules versus frame modules.
113:14 what happens here here is my 1% rock, this is predicting what
113:24 PBS relationships I should get. It's that where I have low porosity,
113:30 know, I have high velocities, should be here as I increase the
113:36 , the ferocity the velocities get And what I find is that I
113:43 to follow this lower bound here oddly . So we'll compare this to our
113:51 . P. B. S. for sand stones. But the point
113:57 , if I have a bride saturated with very low aspect ratio for
114:01 this tells me theoretically that I should above that V. P.
114:06 S trend. So a liquid liquid fractures would pull me above that
114:13 P. B. S trend. , so remember we had the Ramayana
114:21 equation, VP vs. V. . Equation and we showed that it
114:27 with our empirical relation. Um So are the dots And this is the
114:36 porosity Gassman limit. And they agree this tells me is that natural processes
114:47 trying to minimize Watson's ratio. Natural processes are always gonna push me
114:53 this lower bound unless something disrupts those like fractures. Right? So uh
115:04 the rock cooking the rock, having genetic transformations whatever is happening uh to
115:12 rock wherever you're at. You tend be near the lower bound with fractures
115:19 the the exception to the rule. this is a little bit of an
115:32 idea, but if you think about , suppose I was trying to find
115:39 in fractures. It was if I trying to find gas and fractures,
115:45 wouldn't want to be up here. , this has this for this to
115:50 . These have to be liquid filled . So gas and fractures would would
115:55 me on our gas line, it put me down here. So this
115:59 be a way of knowing what can't gas filled fractures. Okay. But
116:12 gets more complicated if we're trying to laboratory measurements, because laboratory measurements are
116:24 not um at the low frequency they're at hundreds of kilohertz or
116:33 And for that we have to use full B O theory. And so
116:39 the equation similar to gas men's but different. So, um,
116:50 different from gas mains equation? beta was our KD over K
116:57 Alright, so instead of one minus squared, you have one minus beta
117:03 this thing with this constant. And added a term in the numerator here
117:12 you actually added what is called an term with the density. I
117:17 Chesnokov likes to talk about density being dependent, it's not really the
117:23 it's the effect of the density on way of velocity is frequency dependent.
117:30 you get another term here and all these terms have ferocity over K K
117:40 the coupling factor between the poor fluid the frame. It's called the mass
117:47 factor. So if K is there's no coupling between the fluid and
117:57 frame and if K is infinity, infinite coupling the fluid in the frame
118:03 perfectly coupled. So what happens if said K to infinity? I get
118:08 mains equation. So, kind of . Alright, now we're going to
118:23 these predictions using these different equations to measurements. Remember I said, the
118:30 you get is gonna depend on the of gas in the pore space.
118:40 how we get gas, how we the gas in in the uh in
118:46 pore space matters, we could inject gas in or we could let the
118:57 in the rock drain out naturally. ? So we could inject Aaron or
119:03 could let the rock dry and let pockets form naturally. And as I
119:16 , when we measure velocities in the , we get a discrepancy from gas
119:21 equations. Uh there's a discrepancy for fully uh saturated rock as well.
119:30 you make this calculation from the dry , you calculate the saturated velocity.
119:35 difference is called non B. Dispersion. Um I'm sorry, it's
119:44 B. O. Dispersion. But there there are also huge differences
119:50 low saturation. So we'll have to about what's happening here now, accounting
120:01 the difference using the mass coupling factor , correct The velocities at 100%
120:12 but won't produce the observed curve, ? All of these are showing an
120:19 off switch, like gas mains but you could correct for the dispersion
120:25 100% saturation by varying this mass coupling . So at least we could get
120:31 point right now, what's happening here has to do with the distribution of
120:42 , how gas is distributed in the . And if we have time later
120:47 the course, we may come back that and show how to calculate
120:53 But we're gonna uh we're not gonna about that now, I'm just pointing
120:59 that that difference exists. So here's example comparing velocities when we in when
121:10 push fluid into the rock, so increase the saturation by injecting fluid into
121:18 rock, or we decrease the water by letting the fluid drain out of
121:25 rock, letting the liquid drain out the rock. And you see two
121:30 different behaviors and that's attributed to different of gas and report space.
121:42 some other things come out of Beos frequency theory, and I expect you
121:48 memorize these equations for the final Actually, I'm only kidding, I
121:54 am showing the equations number one, show that they're complicated but to to
122:01 that there's a plus or minus sign . This is the velocity of the
122:06 wave at infinite frequency. There's a or minus sign, that means there
122:15 two p waves. So according to . O. Theory, we not
122:22 have a P wave and the shear , we have a fast P.
122:27 wave a share wave and a slow wave. And the slow P wave
122:32 slower than the share wave. We've been able to use that phenomenon
122:40 explain things like low frequency shadows under reservoirs, but just pointing out that
122:49 poor elastic wave propagation is not the as elastic wave propagation. So we
122:57 a fast P wave. This is versus porosity measured in the laboratory,
123:03 wave velocity and a slow P Right? This um this slow P
123:11 is what is called an evanescent The reason people don't talk about it
123:17 the reason people don't see it is it attenuate very rapidly. On the
123:24 hand, if it travels a very distance and converts back to p.
123:29 could produce events on your seismic section you won't be able to model with
123:36 P wave modeling. And these are we call low frequency shadows.
123:45 another caution. The frame module asse not the dry frame, You dry
123:54 frame, you change it. It the wedded frame module asse in the
124:00 of the N. C. To fluid. Alright, so I like
124:04 call it the skeleton module asse or the frame module asse. And in
124:10 mechanics they like to call it the module asse. So it's like a
124:17 . I'm squeezing the rock and the are free to escape. They squeeze
124:23 . The fluids come out. So the dreamed modular. Now, why
124:33 this important? Because as we saw that, in that case where the
124:39 wave velocity increased when I added uh fluids can interact chemically with the
124:50 minerals, particularly the clays at low . Uh This has been seen to
124:59 where you could produce silica gels. , if I have quartz grades,
125:04 at low pressure, I add It produces a silica gel on the
125:10 grain and causes the quartz grains to each other. So you could actually
125:17 the frame that way. Um On other hand, if you've ever built
125:23 on the beach, you could pile sand with a higher angle of
125:29 right? You can solidify the walls your sandcastle by wedding them. So
125:35 that case the capillary forces and the tension of the water is actually helping
125:43 the grains together. On the other , water can lubricate the graves.
125:49 I call that the banana peel but that hasn't caught on in the
125:54 literature. But think about, you , if you walk around Houston on
125:59 wet day, you really want to mud because you could go sliding,
126:05 ? So you can buy lubricating the , you can reduce the rigidity of
126:10 rock dramatically, or water can harden frame by causing plays to swell and
126:19 the other minerals more tightly. And of this is handled by gas men's
126:25 . Right. Gas mains equations are mechanical. Now this dry frame module
126:40 um back in uh my paper in the mud rock line paper I claimed
126:48 frame modular Sequels. The bulk module . Some years later. Z.
126:53 . Wang of battle and wang fain out with this uh empirical trend And
127:01 the share module is is .96 times frame modular. So that's pretty damn
127:08 . Right. Um This from a by Spencer showing that for different minerals
127:16 different uh different sediments. He's got relatively small range of lessons ratios.
127:24 For for the frames I um I'm keen on using uh laboratory measurements in
127:36 in brian saturated sentiments to sort out frame ma july. Um I'll explain
127:47 in a bit. Okay so let's a little bit more about the rock
127:56 properties. What controls the rock So here we see that uh as
128:10 increase the porosity, the frame module decreases the frame. Both modular and
128:18 frame share module is decrease. Um are measurements from Murphy again showing a
128:27 clear decrease and so various you could up with various empirical forms to fit
128:35 decrease of the frame modulates with These are a couple of popular forms
128:46 Creflo if have the bulk modulates And sheer module asse given by the ma
128:56 of the rural mineral Times. 1 the process he raised to some
129:04 And so they get a result. this critical porosity model looks like that
129:11 they're pretty similar for low porosity. rocks have different trends though. Uh
129:27 uh has this strand with a very intercept. So presumably this is not
129:37 , I think these were centered glass . Other laboratory measurements, a similar
129:46 as we come out to the 40% . Similar slope courts would be somewhere
129:53 here, but overall a more or linear increase with increasing ferocity. Uh
130:04 might not be so linear if you clays involved. Okay, so um
130:21 on if you try to use uh critical porosity um the question becomes,
130:31 what do you use after the critical ? So what what creep is trying
130:37 do? He's trying to add this here to kind of go towards Royce
130:45 . Right? Whereas the critical porosity model just goes to zero at whatever
130:53 porosity you choose. But you these rocks may have a different critical
130:59 than these rocks. Right? So fit these rocks properly, you may
131:04 fit these. And what about these here, you'd have to use a
131:08 critical porosity. So uh really none these empirical models work for all
131:20 Now we could do theoretical mathematical Uh These are not going to be
131:32 for predictive purposes but they're going to very useful for conceptual understanding of what's
131:37 on. And so you can uh the bulk module asse of the rock
131:46 inclusions being uh related to the bulk asse and share modulates of the materials
132:00 of the individual uh materials making things . But this requires explicitly specifying the
132:13 shape. So you need these factors which have the aspect ratio of the
132:20 in them. So you could but this kind of modeling, as we
132:30 last week, you could model uh example the dry frame module asse versus
132:37 . We just went directly predicted vP . V. S. But this
132:43 a step towards getting there. The ferocity versus dry frame modules.
132:49 you see you're getting these linear kinds trends which are similar to what we've
132:56 . A linear drop in the frame with ferocity. Um And um it
133:04 out that if you have used the tox ohs model with a frame
133:09 I mean an aspect ratio of Uh You get a trend that tends
133:15 agree with what we see with granular . Um This is what you would
133:27 if you had spherical pores. So velocities would be much higher. Now
133:38 this case uh you can add cracks uh to the rock, you could
133:49 I have spherical porosity and now I'm use custard toxins modeling and I'm gonna
133:56 cracks To the spherical porosity. So here we had an aspect ratio
134:02 .1, no spherical pores. All pores had an aspect ratio .1.
134:08 risk spherical pores. So there are hysterical spherical pores. And now we're
134:15 add cracks to that. And what see is a similar reduction in
134:22 But these cracks are much finer and can see how this affects the
134:31 P. V. S ratio. um what you're seeing here in the
134:40 rock is there isn't a big range V. P. B.
134:43 Ratios for the dry rock. In for the dry rock, the cracks
134:51 wind up giving you a lower P. B. S. Than
134:54 spherical for a student. Okay. the range is very small. All
134:59 these are pretty close to both, equal share modular In terms of the
135:06 v. P. B. ratio. The songs ratio is pretty
135:10 to .1 for all of these. that that noise gets to be too
135:22 for you, let me know Okay, good. Because I've got
135:31 working on a deck, I've got cutting down trees and now I have
135:37 lawnmower out there so it's driving me . Okay, now dispersion, I've
135:49 before that if we have attenuation, have dispersion. Dry rocks have very
135:57 attenuation. The attenuation in dry rock caused by solid solid friction. And
136:06 if if I look at wave propagation the moon for example. Attenuation is
136:11 low as soon as I saturate the attenuation increases dramatically because the movement
136:18 fluid and fluid. Solid friction. fact a partially saturated rock has the
136:25 attenuation. Because in a partially saturated the water is very free to move
136:32 compressing gas. So uh if if make laboratory missions as a function of
136:43 , the dry rock velocity isn't changing frequency whereas the these are body
136:51 So the in the water set traded you have high attenuation and the velocity
136:58 with frequency. Alright, so now gonna use the high frequency BBO equations
137:10 try to back out from the velocity what the frame module Ir I'm worried
137:18 if I use high frequency measurements to for K. D. The dispersion
137:26 going to give me the wrong dry modular. Yeah. To do this
137:33 have to know the mass coupling Right? So I'm gonna assume that
137:42 high frequency measurements the mass coupling factor very low The low frequency match.
137:51 I'm gonna set it to one at frequency measurements below frequency measurements. I'm
137:59 assume that gas means equations are So I'm gonna set the mass coupling
138:05 to infinity at that point. And gonna back out the frame module is
138:12 ways and I'm gonna cross plot. gonna do the same for the sheer
138:21 and I'm gonna cross plot. The module is for the sheer modules.
138:26 I do it for the dry rocks I get that trend for the same
138:35 . I do it and use gas equations and I don't get both modular
138:42 share modular. I get both modular greater than share modules on average.
138:51 the other hand, if I use mass coupling factor one, I'm back
138:56 bulk modulates equal share modules. So when we apply gas mons equations
139:03 high frequency measurements and we back out frame module asse we're introducing an apparent
139:10 which isn't real. I'm sorry, an apparent dispersion and apparent difference in
139:25 frame to share modulates ratio, which the difference in the frame worsens
139:31 That isn't real. It's misleading as result. Um your high frequency measurements
139:37 imply a higher poison's ratio for dry stones than you really have.
139:49 so uh you can invert gas mains to determine frame on july if you
139:56 VPN V. S and this will the poison's ratio if there is significant
140:09 . Now there are other things that change uh the frame module this and
140:21 one of the most important things is shape of the pores, which you
140:32 imagine would be strongly related to the content. So uh here We've got
140:44 corpse. These are the empirical relations were observed for sand stones. And
140:53 here we have 50% courts. Here have 0% courts. So, uh
140:59 have a higher ratio of both modules share modular. This is modeled using
141:10 , inclusion modeling. These are similar custom taxes. This is Okano Budiansky
141:17 , Right? The point is the courts, we get pretty much bulk
141:24 Sequels share modular. Um but we clay and that increases things. So
141:30 clay content is important. Similarly, know, kau sai plays muscovite.
141:44 all have higher frame persons. They have a higher mineral persons ratio than
141:53 . So, uh, a significant of any of these other things felt
141:58 far as calcite, micah's will cause sandstone. If I have a dirty
142:06 or anarcho six sandstone, it'll be higher frame poison's ratio. Uh,
142:13 low framed poison's ratio I've been talking um of about 60.1 with bulk modular
142:21 sheer modulates. This is for clean sand stones. Okay, so,
142:31 , how are we going to use fluid substitution while we could use it
142:35 do seismic modeling. So, for , this was something done.
142:45 around late 80's at the company I working and uh, here was the
142:54 V. P V. S ratio a gas sand. This was the
143:01 data. Uh so we're looking at amplitude variation with offset. So
143:07 this is the CDB gather and we're at these wave forms acquired at different
143:14 . And this is the elastic model was produced, the computer simulation that
143:20 produced using the predicted be PBS And if you look at the amplitude
143:27 with on this guy, you could at the, you could measure the
143:33 on the data, you could fit trend to the data, which is
143:37 red curve. And you could look the amplitudes from the simulated model and
143:47 see that they agree with the trend the data. So it's kind of
143:53 verification that the things we're doing aren't terribly wrong. Now. Here was
144:00 case which was interesting because it was oil stand, but it was a
144:05 oil sand and it was very Er So it's V. P.
144:08 . S ratio was higher than the shells, whereas the gas sand,
144:13 B. P. B. Was lower than the surrounding sea shells
144:18 , it's higher. And so rather having uh an amplitude increase with offset
144:25 the gas sand, uh These data a flat A. B.
144:29 Response didn't increase with offsetting and the model showed a similar result to uh
144:38 the data. Another complication that can is as we start producing a
144:50 So if we're looking at seismic data production has started the production can change
145:01 fluid properties. For example. Uh the case where you might have had
145:09 on oil and the pressure is the pressure comes down and drops you
145:17 the bubble point or the oil at case bubbles will come out of solution
145:24 the oil. You can see this has free gas in it. You're
145:29 have to use Woods equation. You're wind up with a very low module
145:33 more similar to the modulates of So here, as soon as you
145:38 that bubble point, you have a change in the impedance of the oil
145:45 rock, a quantum change. So could have a big change in the
145:52 , seismic response as a function of . So we call this a time
145:57 effect. Now, here was a of gas over a brian sand after
146:08 where the is presumed that gas came of solution in the brine. And
146:16 you're getting is a relatively flat variation amplitude with offset not uh an amplitude
146:26 with offset which is often what people . This was the original gas over
146:35 sand before production at least the synthetic of it. All right,
146:41 you can see here the the the V. P. B.
146:45 ratio is dropping in the brine leg gas is coming out of solution.
146:50 , I have to be very careful these things and that also affects if
146:58 use producing fields as analogs for seismic , it could cause you to get
147:07 trouble. So, for example, I have a productive field and there's
147:14 bright spot that the production is coming . Alright now I drill here,
147:21 get a dry hole. I drill , I get a dry hole.
147:26 of these had an amplitude anomaly like . So I go to this location
147:32 I look at the amplitude there and , I've got a little bit of
147:36 here. But compared to that, not this nice, coherent, beautiful
147:43 . I compare this is present day . These wells were on production long
147:50 the seismic data was acquired. Comparing amplitude to that amplitude is not appropriate
147:59 I've changed the fluid properties here by so it would tend to, you
148:06 , if I'm dropping the pressures and making uh the hydrocarbons more uh compressible
148:17 things are coming out of solution. free gas is coming out of
148:21 These amplitudes anomalies are stronger today than were before production. So, you
148:30 , comparing this to that isn't And in fact that was a productive
148:39 , I think, okay, I I showed this example before where we
148:43 gas in the shell. This was interesting case where we were looking at
148:54 near surfaced V. P. And . S. Measurements and we were
149:00 at this over a field and outside field. So the field is is
149:11 below us here. We're in the near surface, we have very low
149:16 wave velocities. Uh And these are . C. Two measurements using actually
149:22 shotgun to to uh create the And uh so we look at p
149:30 velocity versus shear wave velocity over uh the field. We have Lovie PVS
149:39 on the flank of the field. have high V. PBS ratios on
149:43 flank or off the flank outside the extent of the field. The measurements
149:50 making our between our empirical shale trend an empirical brian trend. Right?
149:58 we go over the field and we're suppress V. PBS rations. So
150:05 certainly suppress VP. So the claim that yeah we have micro seeping
150:10 It's lowering the V. P. . S. Ratios more like a
150:14 sand. Remember this is a mixture sands and shales but then something very
150:23 . It's not it's a reduction in . P. B. S
150:26 But you see that the share wave are much faster, right? So
150:34 is you know, seeping gas over field isn't gonna do that. What's
150:40 gonna cause your shear wave velocities to . Well in fact, what was
150:46 here was bacteria was eating the micro gas seeping gas and precipitating cement as
150:58 result of the bacterial activity. So where you had micro seeping gas,
151:06 rocks were more cemented. So be ratio was lower because of the gas
151:13 also uh the sheer sheer the rigidity higher because of the precipitated cement.
151:25 it's the top of the hour. we'll take a 10 minute break before
151:30 wrap up for the day and We'll you at 4:10. So in doing
151:46 substitution, some things to keep in . Question one. What are the
151:56 reading? What are you actually measuring those logs? A density log reads
152:04 a few inches into the formation. if you have a lot of
152:12 the density log has seen the density the invaded zone. So that may
152:19 different than the density of your Sonic logs read a foot or two
152:26 the formation. So they have better . But if you have a lot
152:33 invasion, uh the hydrocarbon effect you may be changed right Even with invasion
152:42 velocities, you still will get, will still have residual hydrocarbons in the
152:48 this invaded zone. So the, know, the velocities will still be
152:55 , but they won't be exactly the as the formation velocities. Uh another
153:04 for this and other reasons, it's better to substitute hydrocarbons into a brine
153:12 than to substitute brian into a hydrocarbon sand. And the brian saying the
153:18 of invasion are not going to be great on the sonic or the density
153:24 , but just in general, sonic tend to be more reliable in brian
153:30 if we're in a gas and we the gas in the drilling fluid,
153:34 attenuate the signal. Also, the of energy into the formation is
153:40 So, in gas sands, you to get a lot of cycle
153:46 you have attenuation in the formation, have poor coupling in the formation,
153:51 have attenuation in the drilling fluid. if the velocities are very low,
153:56 don't even measure the direct wave. mean, I mean, the refracted
154:00 , if you measure the direct way the fluid. So all kinds of
154:05 to be suspicious of velocities in the , sands, brian sands are probably
154:11 reliable. And so if one is to compare the brian sand result to
154:18 gas sand response, you're better off with the brian sand. We already
154:25 about the fact that the density log more sensitive to hold conditions washed
154:31 washed out zones, Rough boreholes, we talked about all of that caused
154:37 density logs to be really bad. sometimes we're better off using the sonic
154:43 to estimate the density than to actually the density log. Now, as
154:49 playing these scenarios of putting hydrocarbons into a brine sand, don't put
154:56 much if it's a Shelley Brian you can't couldn't have 90% gas
155:02 that's just not gonna happen. So in um Shelly rocks, Shelly
155:10 uh, make sure that you consider the residual water saturation would be.
155:17 of course, don't forget that the reliable sonic velocity you could read is
155:24 velocity of the drilling fluid? Uh if the actual formation velocity is less
155:30 that, as you might have in unconsolidated gas and the sonic log is
155:35 giving you the right velocity. so let's go back to doing some
155:51 . So the first one uh should fairly simple um except I'm not understanding
156:04 question. Oh okay, this is woods formula, calculate the fluid module
156:14 . We have to say fluid module . Okay, so this is a
156:22 exercise and we're starting you off easy just calculating um Woods equation. Use
156:32 this oil and a bride module is 3.5 giga pascal's and uh As water
156:43 varies from 0 to 1. See the module us fairies. So we
156:55 stop recording while you work on So what I'm gonna do,
157:03 so what I'm gonna do since this gonna take too long, we'll do
157:07 , we'll start it tomorrow. I'm go ahead and pull up another
157:15 Just let me find it. Let's share. Uh There I go.
157:24 and let me share where is There it is. Chair.
157:37 are you seeing a word file? . Okay, so I think this
157:44 gonna be good preparation for your final these these are the kinds of questions
157:50 get it will all be short answer this multiple choice and true false.
157:56 for interruption. So should I record now? Yeah, this way Stephanie
158:03 review it. Okay so which of following is a hypothesis? A fine
158:12 go more easily into suspension than coarse be as fine particles are added to
158:19 course, sentiment ferocity is reduced. when gas replaces water in a porous
158:25 shear wave velocity increases because of the attraction of the moon. The all
158:33 the above. E. None of above. Would it be C.
158:43 . Very good. Even though it ridiculous and wrong. It was very
158:49 . You're using your brain. Um a hypothesis because it's an explanation right
158:56 wrong of an observation. Good. . Which of the following is a
159:02 theoretical upper bound a the Rammer Hunt equation be the critical porosity model.
159:10 the Voigt average D all of the . E. None of the
159:22 Um I have to go through my , think about think about the word
159:29 theoretical as opposed to empirical see? A that's an empirical equation. It
159:47 as a practical upper bound but it's the strict theoretical upper bound. What
159:55 the widest bounds possible found possible. the low lowest bound possible? Oh
160:08 just went over that. That's Well, okay. Yeah I mean
160:14 was the low I'm sorry that was lowest bound on fluid substitution but if
160:23 have to materials that I'm mixing what is the lowest the modules can
160:30 . Well Okay, yeah you're zero but it may not be possible
160:36 achieve. zero. What is the theoretical possible bound? Do you remember
160:43 Royce void bounds? The Royce bound the reciprocal volume weighted average. That
160:50 the lowest module issue could have and highest module issue could have theoretically is
160:58 void average. That's the void So the answer is C.
161:08 so three the Royce average computed using reciprocal volume weighted average of constituent plane
161:16 , ma july A is a strict bound be greater than the plane wave
161:24 is computing using Royce averages of bulk shear module. I see results in
161:31 suspension of solid particles and fluid having rigidity in a wood like equation D
161:39 of the above E. None of above. We just said A for
161:47 one it's a Yeah, now it's that a suspension of solid particles uh
161:58 , is the Royce bound. But you use uh you know that is
162:04 a strict bound. So that that's we call the wood like equation
162:10 four In poorly lit defied rocks with is below 30%. Which equation provides
162:18 better prediction of velocity from ferocity. gardener sandstone equation be widely time average
162:27 . See critical porosity model. I . I'm smart. I'm just bad
162:35 the spot. Well, you haven't , I've just given you the kinds
162:42 things that you're going to review. if you go back to your
162:46 you'll find that the gardener equation is poorly lit ified rocks whereas widely time
162:54 equation is for well it defied rocks the critical porosity model. Like the
163:00 Gardner equation is a practical upper Mhm. Okay, true or false
163:09 defoliation usually increases anisotropy feeling. This true. Yes. Okay. You
163:19 one of the you know when I this class with you know this
163:22 when I have 20 people, there's a curve. Right? So what
163:27 I what do I do for a when there's one person in the
163:35 The kinds of philosophical questions that I to deal with. Okay,
163:43 So six. What needs to be to have a unique relationship between ferocity
163:49 velocity? A pressure be poor see degree of with indication de
163:59 Yes. Yeah. So you're not badly without studying. That's how good
164:06 teacher I am. Which type of will have the greatest effect on seismic
164:14 per unit volume of ferocity. A be effective C fracture. Mhm.
164:24 it be buggy has the smallest effect size? Yeah. Because fractures are
164:35 compressible. A few fractures. Lower velocity. A lot compared to normal
164:43 . Okay, a true or A shell must be composed primarily of
164:51 minerals which you'll remember from rocks and are fill a silicates true or false
165:01 didn't hear your answer true false. took rocks and minerals 200 years
165:13 So can be primarily courts. Right. They usually have a lot
165:21 clay minerals but they don't have By definition a shell is a fine
165:30 mud rock. Alright, true or . And an icy tropic rock cannot
165:38 definition be homogeneous. Okay, that's . Okay. No it's not actually
165:47 it or not. That's false. an anisotropy. Rock is anisotropy is
165:55 variation of velocity with direction. But that could be the same.
166:02 place. That variation of velocity could the same every place. So in
166:07 ice tropic rock can be homogeneous at macro scale. At a micro
166:14 No rock is homogeneous, right? you could be in poor you could
166:20 ingrained. Right? So uh at you know, at the macroscopic way
166:30 looking at at a rock the anisotropy it's the same every place. The
166:35 is homogeneous. Okay, In the figure. Well, the figure is
166:42 . All right, forget number I don't know what I did to
166:46 figure. Okay, let's get rid that guy. Okay. 11.
166:55 porosity of one has a void ratio 10 or infinity. Mhm. I'll
167:06 you a hint avoid ratios, porosity by 1 - Porosity. Oh it
167:12 be infinity. Okay. 12. is the grain density for Iraq?
167:18 is 50% courts and 50% calcite. 2.65 to 2.87 C 2.71 D.
167:29 of the above. So this requires know the grain densities for courts and
167:34 . And these are numbers that Should remembered is two points Right? Because
167:44 is 2.65. Well cal side is . So it can't, the answer
167:50 be 2.87. It's got to be 2.65 and 2.71. So the answer
167:56 none of the above. Yeah. . I could have like put two
167:59 two together for that one. Okay Assume ice has a density of
168:07 g per cc. What percentage of iceberg is exposed? 90% exposed.
168:18 I was getting coffee. You only the tip of the iceberg and that's
168:26 I was in my head. So don't know why. Okay.
168:32 Which sphere pack has the lower specific area? A simple cubic. Be
168:40 hexagonal. See exact journal close Oh that was cubic because lower specific
168:53 and I think that one's cubic or , I'm like picturing all those things
169:01 my head. Um It's not be think it's a no I don't
169:19 You know what let's go back to place. Let's go find it.
169:29 like looking through all my notes right . Trying to find open. It's
169:40 a while lecture to. No that's . Class. Ah Okay. File
169:53 should be able to find brows I find browse for some reason.
169:57 there it is browse Where's porosity? it is. Unit two.
170:18 This is like a Vulcan review and back bad memories. Right? Not
170:27 all. Okay. We're getting Remember this guy? I am still
170:43 at the test. I'm still looking the test. Okay. I have
170:48 share this. Sorry, where is ? Oh God, hope that's
170:59 Did you see the equation for a surface area? Well, I hear
171:21 so which sphere pack has the high the lowest ferocity. We had simple
171:29 , hexagonal or hexagonal close packed. you remember which of those as lowest
171:39 . Simple cubic is the least exact exact clothes packed is the most
171:46 . Right? So that must be lowest ferocity. So you have the
171:51 . So which has the highest specific area. It would be the clothes
172:00 . So it was a little bit to intuition, wasn't Yeah, I
172:05 picturing just a big old cube. , I see. Yeah.
172:15 Yeah. So these are spheres. just the way they're arranged.
172:22 practice test. I need to re . What am I doing around
172:36 Okay, we're back. So the lowest specific surface area weight.
172:46 lowest specific surface area. One minus . The question was the lower So
172:52 were right in the first place I wrong. The answers answers. Simple
172:59 . I outsmarted myself. Okay. 15 as a sparkle grain increase increases
173:13 size, the ratio of surface area volume A increases or B decreases,
173:23 . Yes, there's a problem for . Wasn't okay, true or
173:32 The sphere pack arrangement has a greater on specific area area than grain
173:40 True. No. Remember grain It's it's three times one minus porosity
173:51 our right. The grain size. I think we did this as an
173:58 for different sphere packs and we found grain size was a dominating effect.
174:09 , cause porosity uh you know, it's three times one minus porosity and
174:16 only varies from 48% to 26%. ? But our can vary by orders
174:24 magnitude. So, so, grain has a bigger effect. Okay,
174:30 or false. A spherical particle has smaller surface area for a given volume
174:36 an angular particle. That is Yes, Yes. The sphere has
174:50 lowest surface area per uh per given than any other shape. I
174:59 think about it. A flat plate angular. Right? So it's got
175:04 high surface area for the volume. . Oh, for some reason the
175:10 didn't didn't copy so let's forget about one. Okay, 19. Most
175:23 reduction with increasing depth is usually accomplished a rearrangement of grains and compaction.
175:30 segmentation sees dissolution, Yep. 20 increasing depth, which of the following
175:40 generally occur. A decrease in point . Be increase of coordination. C
175:49 . A flat or interlocking context. all of the above. E None
175:55 the above. Mm When I say in point context, I should have
176:04 decrease in the number of point I know C is right. Is
176:17 right? Increase coordination. In other , you're contacting more and more grains
176:23 you get buried? Yes. So I can see it's good.
176:29 can see it's confusing without knowing where head was at. When I say
176:34 in point contacts. That seems to contrary to increase of coordination.
176:40 But I'm not talking about the number point contacts. Right? I didn't
176:48 well, no, I wasn't talking the number of contacts. I was
176:53 about the number of contacts that could classified as point context because what happens
176:59 you bury Iraq, you deformed the and you start distorting the grains such
177:06 they're no longer a point contacts. contact is going to be more compressible
177:13 a flat contact, which is gonna uh less rigid than an interlocking
177:20 Okay, next one ferocity and mud's increases with decreasing a pressure. Be
177:30 size C ability to go into solution suspension. D All of the
177:37 E. None of the above all the above. Yes, true or
177:50 . Mont Marila night is a swelling that can have significant nonce Tokyo metric
177:56 water incorporated into the crystal lattice. true true True false Sandstone has a
178:05 porosity of about 15 false. That's . Yes. Remember we have the
178:16 ferocity of 40% or simple cubic Okay. Um I think I've tortured
178:24 enough for this afternoon. So let's it a day and uh yeah,
178:32 know this will all be recorded so will be good review for your
178:37 And also you get familiar with the of questions I asked. Alright,
178:44 tomorrow morning we'll we'll write in early a.m. And we'll skip lunch again.
178:50 we'll wrap up by four and we'll out the day doing fluid substitution in
178:58 . So we're immediately gonna have to up. Okay, so see you
179:05 the morning then. Alright, have good
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