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GEOL7324-Rock Physics - ThursNov4
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00:01 this conference will now be recorded. I believe through this equation and
00:10 I really didn't explain what the terms . Uh and so you guys need
00:15 stop me when I do that. I just forget. And the subsequent
00:24 em accounts for the matrix. The that Custer taxes model works. It's
00:30 inclusion model. So you have a which is the material and then you
00:36 stuff to it. You add inclusions are ill ipso idle and shape furthermore
00:43 randomly oriented inclusion. So it's icy . And plus, as I said
00:49 , it's a dilute solution. The aren't interacting with each other. So
00:55 have a matrix which has both modules the sheer modules. And then you
01:00 inclusions of different shapes that are So on the right hand side is
01:09 summation over the different conclusions. you have inclusions. A volume fraction
01:16 those inclusions. The both module lists those inclusions to share module lists.
01:22 we have inclusion. I you I close one eye equals two equals
01:27 . These are different inclusions with different and different material properties. Right?
01:34 Kay is the material property that's independent the shape for that inclusion. And
01:40 shapes go into these terms the PMI the army. So that's where the
01:49 ratio of the poorest comes into And so what you're doing is you're
01:54 up the volume fraction of pores with shapes and different mechanical properties are different
02:03 module. And so these are on right hand side, on the left
02:08 side, you have the material, know, the background medium that you're
02:13 the inclusions into And then you have effective modules. Uh so,
02:19 asterisk 80 and us Estrus Katie. the bulk and shear molecule of the
02:27 medium, which is the matrix with inclusions in it. And I noticed
02:34 it's not clean because you have the is you're trying to determine in a
02:40 of different places. So you have do a little bit more algebra with
02:45 and solve for the effective modules. it's written this way so that you
02:50 the inclusions on one side and the material properties for the matrix on the
02:58 side. Okay, I hope that's by the way this symbol. And
03:04 forget what that greek letter is. is a complex expression that involves the
03:11 in sheer modules of the matrix. just as a shorthand, it's been
03:17 with that simple, but again, is the material properties of the
03:27 Okay, then we talked about dispersion we said there's a low frequency
03:33 high frequency limit. If we're doing relative to sonic logs, where we
03:40 be in the kilohertz range, seismic would be, you know, tens
03:46 hertz. And laboratory data could be of kilohertz or megahertz. So we're
03:55 to assume that with laboratory data were to the infinite frequency velocity up
04:04 So there's a difference in velocity between where we think gasman is applicable.
04:11 the laboratory measurements. So we need equations to handle these higher frequencies.
04:17 gasman is down here? It's the frequency limits. And so this is
04:24 are the equations I showed you before there. They reduce to uh gas
04:31 equations when this kappa, which is mass coupling factor. When this goes
04:37 infinity, this term disappears. Uh , there's a typo here. That
04:44 be too Yeah, that should be times ferocity over cap of the parentheses
04:50 be outside. Let's go back to I just caught that. I've only
04:54 showing this for 20 years. Let's all the way back. Yeah,
05:01 Ferocity over Kappa. So come back . All right. And then also
05:08 modification of the density due to the differences between solid and fluid. Uh
05:15 will also cancel out so, vast factor of infinity means infinite, infinitely
05:23 . Right? And that's what happens zero frequency. The fluid and the
05:29 are moving together, but we go higher frequencies and the fluid and the
05:35 start moving out of phase. Uh , uh if we carry it to
05:40 extreme, we could say no coupling the fluid and the solid, In
05:47 case we would set Kappa equal to . So these are the two extremes
05:52 as you vary capital, which is frequency dependent. You would very capa
06:00 From infinity at zero frequency to one infinite frequency. So you could with
06:09 you can handle the dispersion? All right now. Sorry about
06:19 Yeah, I need to get a typist. But this was all type
06:23 years ago. I was probably the , which was a mistake. All
06:28 . Moving ahead. Um, I talked about using uh Beos high frequency
06:36 to get at the dry frame All right. So, we could
06:43 . These are clean sand stones for sand stones. The balkan sheer module
06:48 are about equal. So, from U. Is equal to about
06:53 . The B. P. S. ratio would be about 1.5
06:58 ratio would be .1. And remember said that if you're clean as we'll
07:04 in a minute, you add other and that ratio will increase. On
07:09 other hand, if you uh, gas men's equations with ultrasonic data,
07:16 not what you get. You get mu bigger than one. All
07:21 So, you get to mislead, get misleading dry frame properties if you
07:27 gas mains equations because they're not applicable laboratory frequencies. However, if you
07:34 videos equation And you assume a mass factor of one then you find broken
07:41 modules are equal again. So, pretty confident that in clean sands towns
07:48 can assume with the PBS ratio of 1.5 or Ko from U equals
07:56 All right now. Uh That's comparing to seismic frequencies. Where do sonic
08:06 belong in that. Are they in low frequency regime or in the high
08:12 regime. and in the early 60s looked at this problem and they concluded
08:19 stomach dogs were in the low frequency in porous permeable sand stones.
08:26 their analysis was based on brian saturated and there's a lot of evidence to
08:32 that if you have partial saturation or saturation uh that you may in fact
08:40 be in the low frequency regime. could in fact be on uh uh
08:47 the dispersal of range where the frequency the velocity is varying with frequency.
08:54 , so uh if you're inverting gas equations for elastic module light and you're
09:02 at the low frequency limit uh then overestimate the Hassan's ratio. Uh If
09:09 is significant dispersion and the jury is out on that, we we don't
09:14 have a well log that measures dispersion . We try doing this many years
09:22 . There are sampling and resolution It's really hard. If you were
09:26 a homogeneous medium you could have a source at different frequencies and it be
09:33 easy to see the velocity dependence on . Uh huh. You could do
09:39 by spectral analysis but there are all of geometric effects in the borehole.
09:45 the jury is really out on We we don't know how much dispersion
09:49 is check shot seems to indicate that have a few percent dispersion but it
09:57 be a lot higher where you have compartments And again that that is an
10:02 that is not well documented. now looking at this ratio between balkan
10:12 module is ted smith did some uh modeling, we talked about Custer
10:19 Does there is a similar type of called the O'connell and Budiansky model.
10:26 calls it Budiansky and and O'connell um Similar idea adding penny shaped cracks to
10:35 inclusion. Not exactly the same but results. And what it finds is
10:42 if you add other stuff. Uh . Two if you're pure courts you
10:52 to have equal bulk unsure module. but if you add other materials that
10:59 like clay you could increase the bulk is relative to the share modules.
11:05 these are of the frame. So dry friends And here is being very
11:12 about the minerals he's adding. So here we have courts which was
11:20 persons ratio. V PBS ratio of persons ratio 0.1 corresponds to a V
11:28 . B s ratio of 1.53. say courses down here Someplace in the
11:34 of 1.5 Fewer courts or v. . b. s. to
11:39 Um Now as you decrease the amount courts and you add other minerals is
11:45 muscovite which should be somewhat similar to . Uh Not exactly, but he
11:53 properties from muscovite. He's added calcite he's adding flour to replace feldspar.
12:00 he's getting a dramatic increase in the . P. B. S ratio
12:06 the dry frame. Uh And that's the minerals have higher fluorescence ratios.
12:13 if we're talking about inclusions in a background, then the minimum module is
12:19 going to be very important. Remember we were talking about sphere packs,
12:24 mineral module list didn't have a big on the V. P.
12:28 S ratio of the dry spear But if we have a cracked solid
12:34 a solid with inclusions in it, the mineral V. PBS is going
12:38 be very important. And you can it basically almost linearly varies between the
12:44 . P. B. S of , and the V. P.
12:47 . S. And the other mineral mixing. So the moral of the
12:51 is if you have, if you have a clean coarse sandstone, you
12:57 have a higher persons ratio of the . Now, uh we talked about
13:07 relate transformations and so forth and fluids we're producing a reservoir as pressures are
13:15 , there's the potential to have sudden in the phase composition. So for
13:22 , here you might have gas on of oil. Uh This would would
13:27 been in equilibrium uh in geological equilibrium the time you drill well and suppose
13:36 start dropping the pressure, then the could come out of solution in the
13:43 . And keep in mind here, have a big change in the bulk
13:48 of the fluids. The gas is more compressible than the oil.
13:54 this could have been gassed over brian theoretically could have some gas dissolved in
14:00 brine, especially if it's fresh and very saline. You drop the pressure
14:06 gas could come out of solution of oil most likely, but it's also
14:11 could come out of the bride. now remember Woods equation we we produce
14:19 few gas bubbles here and now the leg. Then we'll have very similar
14:26 to the gas legs. So immediately production, we've got big changes now
14:32 enhanced oil recovery where we're injecting, saw we had pressure fronts where you
14:38 pressure increases and as you produce you have pressure decreases. So it could
14:44 out to be a very complicated Just as an example, the effect
14:51 we have gas over brian stand and we produce the gas. Maybe it's
14:57 depletion drive. We don't have a water support of the pressure. Maybe
15:05 brian leg is not well connected. an isolated compartment. So you have
15:11 depletion and gas starts to come out solution from the brine in this case
15:17 it changes the seismic response totally. . And this could happen on primary
15:27 , where the rock fluid properties are . And I've seen this happen a
15:34 . Where here we have a recent section at the time? It was
15:41 overproducing fields and there is a bright associated with the production. And now
15:49 want to explore. There was a hole here and a dry hole here
15:54 you have some weak amplitudes over Now in exploration, we'd like to
16:01 analog as we like to look at we have production, see how that
16:07 manifests itself in the seismic data. here we see that there's a weak
16:14 , but it's not nowhere near as and coherent as this aptitude here.
16:21 might cause us to be pessimistic about location over here when in fact that
16:27 drilled and it was packed and the in the use of this as an
16:37 is that this is what the seismic looks like after production, but this
16:43 before production. And if production has the fluid properties, it could give
16:50 a different response. So, and tendency would be for things to brighten
16:56 as you lower the pressure. So use uh using analog is where you
17:03 recent data after production could cause you be pessimistic about your prospect. So
17:10 you probably need to model those changes pressure versus current or pressures at the
17:18 that the size was acquired. one thing we find is that gas
17:30 equations are a little bit problematical and , if you think back to the
17:38 of gas mains equations, uh, that the pore pressure would culebra rate
17:45 the pore space. If you have shell, that's very low permeability.
17:57 , during the passage of the there may not be time to celebrate
18:03 pore pressures. And so these are data. And what we find is
18:10 if we cross plug VP vs. . S in shells that have gasped
18:17 them, we find a suppressed Pds ratio relative to the wet show
18:23 of the presence of gas, but as far as gas mains equations would
18:30 predicted. So if I took the rock line and a velocity porosity transform
18:36 I predicted using gas mains equations. what the corresponding gas share line would
18:44 , what I find is, I quite make it. I'm in between
18:48 two and and so it has to with the lack of pressure calibration in
18:55 shell. Um Now, this is controversial subject. Um I've published with
19:04 of my students examples where it seemed we were getting good correspondence using gas
19:12 equations. The problem is that as we saw before in low porosity
19:20 , gas once equations could be very , uh if we have a slight
19:27 in ferocity. So how well do really know the ferocity in order to
19:32 a fluid substitution. This was another where we were in a largely shell
19:45 but it's these data were from high DSPs In the near surface at two
19:52 locations. Uh had a well away a producing field that was a dry
20:01 and then in a well above producing . And we're looking at the relatively
20:07 surface sediments. So here we have shale trends here, kind of like
20:15 mud rock line here we have our brian stand trends. And the VSP
20:21 were clustering for the well that was from the production. We're clustering over
20:27 where we uh we have fried saturated and for the well over the
20:33 we saw a variety of points in . Now interestingly, uh the difference
20:42 these points and these points was more the sheer velocity then in the P
20:48 philosophy. So you could not fluid these and get this. This actually
20:58 implies a different rock frame. And explanation here and there was geochemical data
21:04 suggest this was true, is that had microbial action on the micro cp
21:12 above the reservoir that were precipitating And so uh these uh this location
21:22 more heavily cemented than that location and result was an increase uh in the
21:28 wave velocity over and above the fluid . Uh huh. So essentially the
21:38 and the fluid effect almost canceled out in the P wave velocity. But
21:43 see the segmentation in the sheer weight . Alright. Some practical suggestions when
21:57 fluid substitution. I already mentioned how logs can be unreliable in gas
22:06 Remember we saw that example where there cycle skipping. There are a variety
22:10 reasons if you have gas in the bore the gas bubbles cause cause scattering
22:16 with your sonic signal. When you Lovie PBS ratios like in the gas
22:22 , the coupling of acoustic energy into into the formation is also reduced.
22:30 that would give you a lower amplitude . And um there's also the question
22:37 invasion. Right? So remember we mud cake. We have a rule
22:45 borehole. And we also have an zone around the borehole. And that's
22:51 clog is a refraction experiment. And you remember from geophysics 101 when you
23:00 a high velocity layer, uh your waves don't penetrate down into an underlying
23:07 velocity layer. Right? So if have invaded the formation, pushed the
23:12 away from the well poor, the log is going to read the faster
23:19 if that if you were able to all the hydrocarbons away. Um So
23:24 the potential for that to happen. The death of the log uh you
23:32 , doesn't see through the infected it only sees a few inches into
23:36 formation. So for a variety of we we suspect are well logs uh
23:46 our reservoirs. Unfortunately we suspect our log and our sonic log as being
23:52 of what a seismic wave we'll see from the surface. Uh, so
23:58 that reason we're asking for trouble when start with the gas damn velocity.
24:08 let me, I hate to do . We're gonna do a balkan
24:13 mind scan here. We're going to into very quickly. Go to the
24:19 of No, I can't, I it up. You can't do that
24:28 . You can do it in Okay, yeah, let's get out
24:32 go back to here. Another reason you have low velocity sentiments. Another
24:40 why you're gassed and velocities are suspect again, because it's a refraction
24:46 the sonic log can't read velocities lower the drilling mud velocity. So I
24:52 that in this case these gas fans , the actual velocity was actually much
25:00 . But what's being the stomach log seen as a direct way through the
25:05 mud. And so you get flatlining right at the velocity of the drilling
25:11 . So in fact, maybe the here was 3000 ft/s. But the
25:17 log is reading 5000. Now, you do fluid substitution and you start
25:22 5000, there's a chance if you to predict the brine stand velocity,
25:29 a chance you would predict something much than the actual brian. Stand
25:33 Whereas if you started with the correct and velocity, you might match the
25:39 stand velocity. So the moral of story is um don't start with your
25:47 , sand and fluid substitute to Start with your brine, sand and
25:52 substitute to gas. Right? The , sand velocities are far more likely
25:58 be nearly correct. We talked about logging early on in the course.
26:07 in mind that the density log is , is not designed for seismic
26:13 very sensitive the whole conditions. So very suspicious of your density log when
26:19 use it for seismic applications. Sometimes better to predict the density from other
26:27 than to use the actual density law you're doing fluid substitution. Don't be
26:36 in the types of hydrocarbon saturation, that you would get uh if you
26:42 a very clean formation, you could a very low water saturation, but
26:47 Shelley formations there's usually a lot of you know, residual water. Uh
26:56 . So you would uh it's unusual get water saturation in the Shelley formation
27:05 much lower than 40%. Okay, keep in mind that you can't measure
27:12 that's slower than the drilling mud. , I've mentioned repeatedly that there's something
27:24 about the reindeer Hunt Gardner equation. we said the reverend Gardner equation applies
27:30 highly liquefied rocks. And uh huh you could do a ballpark fluid substitution
27:44 by varying the fluid velocity in the behind Gardner equation, whereas that will
27:50 not work with the widely time average . So, I was just curious
27:56 if we had rocks that obeyed the martin Gardner equations. So I have
28:02 I'm plotting in brine stand velocity here ferocity and uh I then do fluid
28:11 using the Raymond Gardner equation. So the lavender line there and then I
28:19 compared it to my empirical relation that talked about last time. And we're
28:24 to look at that again in a and it turns out that they agree
28:30 well. So at least in well ified rocks, it looks like if
28:36 if you're a fluid substituting to you can get very close to the
28:40 answer using the Ramen Hangartner equation or empirical relationship. Again, this would
28:48 be right in well with the five . All right. So, we
28:55 a bunch of exercises on fluid So, let's just walk through
29:03 Um the Yeah, this is going be a lot of work.
29:08 so get to this as soon as can. Um So, I'm asking
29:15 to calculate the effective module list of uh oil water mixture. I have
29:23 properties here that have been put out Mike vassals fluid properties program. It
29:28 the predecessor to U. H. . Flag pro program that came out
29:34 dr hans lab. Um So there fluid properties that are a function of
29:43 pressure, oil gravity, gas, ratio, gas gravity. Uh and
29:51 result is you get a modulation giga that's this one, 1.2835 Compare that
29:59 water, which Insanely that that could 3.5. Right? So we have
30:04 big difference between oil and water here you're going to mix them as a
30:12 of water saturation using Woods equation. that that's all you have to do
30:17 exercise and I'm one just to fly equation, same equation you used for
30:23 suspension. Previously, you're going to use it to mix too fluids,
30:30 bubbles of one fluid in the Okay, Next, we're going to
30:38 do a fluid substitution using gas mints . And so I give you a
30:46 wave velocity and a ferocity. And You're going to so this is for
30:55 100% brine, saturated rock And you're to predict the velocity at 50% gas
31:04 and you're going to do it as for different uh gas ma july and
31:12 . And so you can start uh this And uh use a water saturation
31:23 50%. And yeah, I uh let's see, we have row
31:33 and Yeah, I'm just telling you have a gas modules for .1 and
31:42 vary that and see what happens. and uh the same outline that we
31:47 through a couple of times previously. just repeated it here for your
31:53 I suggest you can either use K mu que dry equals you. Or
32:01 could try to invert for K. from gas, those equations, but
32:07 that you're going to need DS, I didn't give you, but you
32:11 get that from one of the B V s trend curves. Okay,
32:19 . Uh, it's a case where know the brian sand velocity and we
32:24 the gas and velocities and we're going compare these two gas moves equations and
32:31 think we know what the appropriate rock to use our um, but we
32:38 not be right. So the idea to take a first guess with what
32:44 think the rock and fluid properties we're going to try to from the
32:50 sand velocity, we're going to try predict the gas and velocity and then
32:54 going to play with the parameters to if we could get a better
32:59 So, um, if the result get suggests that the dry frame,
33:09 modules is much greater than the dry of sheer module lists suggests the reason
33:15 that might be true. Okay, we could do fluid substitution on the
33:26 equation and that would give us a gas sandstone equation. So, if
33:33 have the garden of VP density trend sandstone and my VPs trend for
33:41 um you could vary VP and you estimate density and from that ferocity,
33:48 clean sands, you can also get share module is from the, from
33:53 DS and the density. Then you everything you need, you could get
33:59 saturated, you could use gasman the is there in your notes to get
34:07 uh huh the both modules, the frame module is and then you could
34:13 back to get the gas man built lists uh, fluid substitute density also
34:22 get the plane with modules for gas for gas. And so now you
34:28 thought the gas dan P wave velocity the gas and density and compare that
34:36 the gardener equation. And as to question, how important is it to
34:43 whether you have a gas stand or ? Is it safe just to use
34:47 gardener? Uh huh equation. Or I do I need to take into
34:55 the fluid substitution by the way for the gardener equation here, you want
35:00 use the sandstone Gardner equation. And uh that that is in your
35:08 . And remember we modify them to through the courts point and uh for
35:17 same uh extending this exercise, uh the same thing with the calculate p
35:26 velocity versus saturation using Gassman and the saturation model. And just discuss how
35:36 differ. Okay, then, I some real world examples. So these
35:46 cases that were encountered by exploration ists uh, it causes you to
35:54 you know, it's a real world as opposed to a textbook problem.
36:00 there may be too little information, may be too much information. So
36:05 going to have to sort through all that and come up with an answer
36:10 . So, uh, so here go. There is a well that
36:16 a clean sand with 60 ft 24 gravity crude and a low gas oil
36:27 At a depth of 70 500 The oil stamp velocity was 11,000ft per
36:36 And there was no porosity log, the corporate city was 24%. When
36:42 say no porosity log in the early , maybe they didn't read neutron
36:47 Maybe they just relied on sonic And you know, we're trying,
36:52 don't know what the effect of the is. So it's a little bit
36:57 until we figure things out what the is just from the summit velocities.
37:04 that well drilled through the oil water and found brian stand with a velocity
37:11 13,200 ft per second, but they have a porosity log. Sometimes drilling
37:18 won't allow you that, you drillers are worried about density, log
37:22 and things like that. So there's big change in velocity is that due
37:30 um the difference in fluids or uh couldn't be that the rocks are
37:37 different deaths. Well, the look the same on the gamma ray
37:44 . And if you take the brine and take the oil properties. Remember
37:52 low G. O. R. very light gravity then. So You
38:01 an oil stand velocity of 12,800 kenya, you're seeing Velocity of 11,000
38:14 . So the velocity change is a bigger then uh things to be
38:22 So what could be causing that Does everybody understand the question When I
38:36 substitute? It's almost the same But the logs were showing me a
38:40 difference in velocity. I need a to explain what's going on.
38:52 Okay. Another case here we're shallow the gas stand has a velocity of
39:02 microseconds per foot And very high porosity . Um brian sand very nearby had
39:12 porosity and was almost as slow. my uh microseconds per foot. The
39:20 logs in the two sand appeared almost . The density was slightly lower in
39:26 gassing. If you substitute brian for . So I start with a gas
39:34 velocity of 50-60 ft/s. And I gasman flew substitution, I get 7400
39:42 per second but I only measured ft/s. So why, why the
39:50 , why is my predicted brian stan much higher than my observed brian standard
39:59 And explain what's going on with the logs, we have a high porosity
40:06 . The gas hand is slightly lower . Then the brian stamp.
40:13 I understand the problem or can explain these measurements. Okay, another
40:25 A clean oil sand was drilled in North day and it was launched to
40:30 the velocity of 9800 ft per second a ferocity of 32%. It's a
40:37 stand and it's filled with oil. Api gravity of the oil was 35°
40:44 the gastro ratio was close to the point brian filson, immediately beneath the
40:53 , sands had the same velocity and and density. Uh huh. Should
41:03 , do you need to do uh substitution. Can you think about what
41:08 of complications might be going on? uh if you explain your answer.
41:20 , last one of these, A stands was encountered at nine around 9000
41:29 . There was minor gas detective in sand during drilling, but not enough
41:33 appear on the loss. Um It a significant amount of gas to show
41:40 as a resistive anomaly. Remember if have an on off switch in
41:47 um you may have a few percent saturation that you don't see on your
41:54 laws, but the velocities of the were measured uh, Velocity 10,000ft/s
42:04 30%. Uh the sand was 55% Quartz, 45% clay water saturation
42:14 one. Um to estimate the effect the gas from the sand, A
42:22 saturation of 90% was used. And predicted Gaston velocity was then computed to
42:29 90 300 ft/s. Um What errors have been made in this calculation?
42:36 you sure of that number or what do you have about that number?
42:44 , Was something procedurally perhaps done Okay, so those are more thought
42:57 . Uh, now, we'll want do some computations and compared to some
43:03 . So, uh, we have table here for a particular stand and
43:10 could tell you in advance the sand very Calgary us. So it's not
43:17 clean sand situation. And so it's you some rock properties, some
43:25 uh, VPN Ds yeah, on water saturated rock and on the dry
43:32 . And so, uh, predict water saturated velocities from the dry velocities
43:37 predict the dry velocities from the water philosophies. So go go both directions
43:45 draw some conclusions. Okay, I gave you an empirical equation, if
43:57 know the brian stand velocity, I get a ballpark estimate of the gas
44:03 velocity. Um So here we have measured velocities compare to this equation and
44:12 compared to the math the equation. that's really uh, prepping you for
44:18 has come. We're gonna be comparing these approximations in a bit.
44:30 now, we have a bunch of here in bryan stand, shale and
44:36 sand. Sometimes the gas sand is across the water contact from the brian
44:43 , but sometimes it's just the nearest sand to the gas hand, because
44:48 we don't have a water contact. the nearest brian standing gas. And
44:55 again, they're not necessarily uh the piece of rock. So keep that
45:01 mind. But it's a nice set measurements representative worldwide collection of gas man
45:09 and brian stand velocities associated or at nearby bryan stand velocities. So go
45:16 and uh, make the predictions. , uh, assume the Visa queen's
45:26 , which they're not necessarily um I'm sorry. Yeah, okay.
45:36 , so calculate the gas fan velocity the brian sand velocity using gas math
45:41 , my approximation in the Mathare approximation compared to the measured velocities, graphic
45:50 , draw some conclusions. Now, if we are assumption about the clean
46:05 is wrong? What do we Right. And how important is it
46:10 we assume? What kind of errors we going to get in gasolines equations
46:15 we um make the assumption the sands clean and they're not. So,
46:20 going to ask you to do a substitution on this rock using gas moves
46:27 , assuming you have a clean So you could say bulk and share
46:32 are equal. But if I had mythologies, I might have other relationships
46:39 balkan share module by the way, to 10 times per centimeter squared is
46:45 pascal? That's so use these different and see how much your fluid substitution
46:55 changes. All right. So how was it that you got the
47:00 Right, okay then. Um moving into kind of direct hydrocarbon indicator
47:14 And here are some models that came Hampton Russell and they had some block
47:23 of P wave velocity density, P impedance, peewee reflectivity and synthetic.
47:32 And also share wave uh huh density share reflectivity. So um what kind
47:41 rock is this layer here? So the interpretation from the blocked model and
47:49 thing here. Make the interpretation from block model. All right then some
47:57 up exercises based on everything we've talked so far. I want you to
48:02 some curves like so if I plotted wave velocity versus fluid density as I
48:09 from gas to oil the water, would the velocity change as I changed
48:14 on the average? How would the change as I increase the age uh
48:23 depth ratio. How is the velocity ? As I change saturation ferocity,
48:30 of segmentation, increasing poor pressure, pressure sends built ratio. Um Most
48:40 these, you'll assume everything else is constant when you're varying the sand shell
48:45 , show you will vary the ferocity and take a crack at completing this
48:56 . So again, all else remaining as I'm varying certain things. Head
49:03 the PVS density and D. PBS if I'm in a classic rock or
49:10 I'm in a crystalline carbonate rock. I started it right. So you
49:17 need to uh complete the direction and talked about this one already. But
49:27 as a review I'd like you to through it again. So look at
49:30 plot, we have velocity these a measurements. So we have brian stan
49:36 and dry velocities. And you see we're more straight up and down.
49:43 the rigidity changes increases as we get we drive. Sometimes the rigidity
49:50 So explain these points. Uh Just make an interpretation as to what's
50:01 . Yeah. Okay, well, we have a little bit more
50:05 So I'll go on to the next which is again, we're still on
50:10 substitution but the next topic is stochastic substitution. So the idea is this
50:18 pretty traditional to start with the Well, log apply gas mains equations
50:28 predicts predicts the gas well off. we get a synthetic for the brian
50:34 synthetic for the gas man. And exploration practice this is often called the
50:43 response. Now, the fact of matter is there is uncertainty in gas
50:51 equations and given the uncertainty and the parameters to gasman and the natural variability
51:00 what the brian response might be, can have a wide variety of gas
51:06 and if you're gonna risk if you're to evaluate a seismic response and you're
51:12 to try to assess the probability that gas. You really need to think
51:18 the variety of Ryan responses you could in the variety of gas responses that
51:23 can have. And so one component that is looking at the error propagation
51:28 gas plants equations. What if I'm on my inputs to gas plants
51:34 how much is that going to change gas response? And the answer
51:39 I'll tell you in advance, the is it can be enormous, especially
51:43 low porosity. So rather than doing single gasping substitution, we're going to
51:50 it sarcastically. So in this case numerically rather than doing one substitution,
51:59 did about 2000 substitution and where we into account the uncertainty of the input
52:07 . Um Now we didn't provide a density function in describing the uncertainty.
52:20 a little bit more realistic to just we could be in a uniform Range
52:27 we could have a uniform distribution within certain range. So, for
52:31 if I give you a ferocity of , It could be anywhere between eight
52:36 12%. Um, you could add and, you know, make a
52:43 or bell shaped type distributions. But the end, your results are going
52:49 be pretty similar. It's more important recognize what are independent distributions and what
52:56 correlated distributions than the exact shape of distribution because, you know, central
53:02 theorem, you're going to be dominated the mean values anyway. And so
53:09 just gonna assume uh uniform distribution. equally probable within a realistic range.
53:18 uh I really don't think that's very . Also, we're going to assume
53:28 of these errors are un correlated except ferocity. That's and we're going to
53:33 that that's highly correlated to density. , so what are the parameters were
53:40 into gas routes equations? Well, wave velocity for the brine stand and
53:47 typical brian sands. Arab put it way, repeatability or error bars on
53:54 measurement on the order of 2%. so uh this might be a realistic
54:02 for kilometers per second plus or minus . That's pretty accurate. Shear wave
54:09 are slower, but the error is less. And the error in shear
54:16 velocities is can be significantly higher percentage . So, but we're going to
54:23 it's the same magnitude Here. So plus or -11 collaborators per second density
54:34 . Remember we said uh delta rho than 0.5 g per CC. We
54:41 believe it. Uh huh. And the uncertainties were going to say,
54:46 , that's the log is good Plus the minus point oh +33 g
54:51 centimeter. Uh That's unless it goes bad. But we're assuming that the
54:57 logs really horrible. You're not going be using it. Right? So
55:01 is where you think you have an density loss. So I'm gonna go
55:05 assume that uncertainty. Um Prosise my , you're rarely better than to porosity
55:14 it. And so I could I could have an average ferocity at
55:18 plus or minus two ferocity in its 30% plus or minus two ferocity in
55:24 to porosity units is probably as good you get. So when the
55:28 these get very low, that's a percent error. So, but I
55:34 that's realistic because in making that ferocity , there are all kinds of
55:41 We have the solid grain modules, of course depends on the composition and
55:45 don't know exactly what the composition of is necessarily. So we're going to
55:52 conservative in this case and say plus minus two giga pascal's on the mineral
55:59 list. We're going to assume we perfectly the brian modules. That that's
56:05 big assumption, but I'm trying to conservative here in my errors. I'm
56:10 going to ignore error in the grain lists, assume I know the water
56:15 list. And another big assumption. going to assume I know the properties
56:22 the hydra carpets. I also, I'm assuming the initial water saturation is
56:29 . So I truly have a brian and another thing that's usually not well
56:35 at all, especially when you're prospecting the water saturation of your prospect,
56:40 I'm ignoring all of these errors. , these are the only Arizona considering
56:46 grain module is porosity density, VPN I'm assuming I know everything else
56:53 And let's see what kind of error produces in my stochastic simulation. So
56:59 started with a Brian stand velocity of km/s. And what I find is
57:06 some of my simulations actually increase the unrealistic. But that would have
57:12 you know, perfectly spherical pores for . Um, so this is where
57:18 started at four. So that O for original, that's my original p
57:23 velocity, mm hmm. The exact solution using the mean values, assuming
57:32 had perfect measurements would be there At km/s. Uh huh. My approximation
57:40 this case gives you 3.82. So pretty close to the right answer.
57:46 , just so happened that way. didn't force it that way.
57:51 math o approximation in this case is little bit off. It could go
57:56 way. Some sometimes Matthew is going be more correct than Pakistan, but
58:02 moral of historians, the approximations are if you like math co or if
58:09 like Castagna, you're still within the within uh, the error bars of
58:18 prediction anyway, so, um, the approximations are close enough.
58:28 now, let's uh, add one , let's say we're not sure exactly
58:33 the bulk modules of the water And we don't know exactly what are
58:39 properties are, By the way, don't let the gas module lists get
58:44 than zero. Right? So we're to truncate this at zero but it's
58:49 to be as high as close to and as low as zero.
58:58 wow, it's nuts. Absolutely Now, what was different about this
59:15 ? Well, the uncertainty in the parameters resulted in this huge tail over
59:22 . Uh huh. I mean, at that range, absolutely enormous.
59:32 the way I presented these results at E G and Z W wang stood
59:38 , you know, bachelor long Z w wang stood up and said
59:42 don't believe it can't be that Um Here's a lower porosity rock.
59:51 the percent error in ferocity is Uh Again we're only considering grain module
59:59 up and just huge variation uh in case uh Monaco was exactly equal to
60:13 the exact result and my approximation was . But again, both are within
60:20 distribution and adding more uncertainty. Oh sorry. Now we've got a low
60:30 rock and you would think things would better at low velocities well. But
60:36 in mind, remember we saw that effect of uh poor shape was enormous
60:43 these low velocity rocks. So lots of uncertainty and all the parameters
60:51 just an unbelievable range in the possible . So um you know, you
61:02 be very, very precise in your but whether that is close to reality
61:08 not, you know, you could the most sophisticated equations. But if
61:13 number is going in or wrong, what you get out is going to
61:17 wrong. Maybe you don't know the that well. Maybe you don't have
61:23 control over all of these. In case uh maybe just taking a rough
61:30 using one of the approximations is good . And by the way, this
61:37 all assuming that the gasman result is correct answer. Remember we've in gas
61:47 equations were assuming the pore pressure we're assuming a single mineral components.
61:54 you have multiple mineral components uh that wildly different properties, we have the
62:00 get a lot more complicated and there is no general solution. There are
62:07 cases where we have solutions but not general solution. So we don't really
62:13 how correct guess whose equations are. they don't take into account this
62:18 L angry at slumber. She thinks seen in version and not taking into
62:25 invasion. So, you know, tremendous uncertainty in the fluids institution.
62:35 , the uncertainty can be larger than predicted change in velocity. Uh,
62:41 is the range of outputs is usually than the errors in the approximations.
62:48 so as a result, when we high department indicators, we need to
62:53 at these statistically we shouldn't have one for what a gas, My prospects
63:01 look like, there should be a of answers. And then from the
63:05 of answers, we should calculate a that you have hydro purpose and if
63:10 have time before the end of the , I'll show you how to do
63:17 . That would be our last which would be advanced applications.
63:23 odds are we won't get there. haven't gotten there in years. So
63:28 , but there, but you can with the uncertainty. And I've published
63:34 couple of papers on that. just to summarize and then we'll go
63:44 for today. Grassroots equations are not applicable. A lot of the assumptions
63:53 violated. Um if you have highly mineral components, we don't know if
64:00 work if we have low fluid mobility the low permeability, zor, high
64:05 is that's a problem. Invasion, , et cetera. We have high
64:11 to input parameters which can be significantly error. Um We haven't taken into
64:19 remember Gaston's equations are purely mechanical. haven't taken into account possible differences in
64:26 genesis and geological history between the gas brine saturated rocks. Remember I showed
64:32 the case where we had more cement where we had hydrocarbons due to microbial
64:38 . So, you know, that absolutely not taken to accounts if we
64:44 to be at low effective stress, can be chemical effects like repulsion between
64:51 , there can be capillary effects. we could have framed hardening or softening
64:56 we, especially when we have Shelley , um we haven't, you
65:03 we've assumed that the fluids are homogeneous distributed throughout the rocks. Um We
65:11 talked about the patchy saturation model and we have time in talking about
65:17 I'll show you the effect of Uh homogeneous distribution of hydrocarbons between four
65:25 All of these results in woods equation necessarily being applicable. Uh I also
65:33 to point out that fluid substitution is the wrong exploration question. Yeah,
65:40 exploration question is not. What is difference in response between hydrocarbon saturated rock
65:48 a brian saturated rock? The exploration is I have uh an amplitude of
65:55 certain magnitude, what is the probability gas or its prime? Now that
66:02 are two very different questions. And fact, if I'm comparing to
66:08 I have a bright spot, that's dry hole, I have a bright
66:12 , that's pay. Um is fluid ? The answer to that question?
66:19 not. So you have to think rather than the fluid substituted brian
66:25 you have to think about the equivalent sand, What brian sand would give
66:29 the same response as the guest? , well that's all I have for
66:35 , Are there any questions in which I'll let you go question.
66:46 I wanted to make sure I was along correctly, it was actually thinking
66:50 an example. So I have a northwest of Australia and it's, I
66:57 a hard Marley section and then underneath I have a bunch of sadistic
67:01 alluvial gas field but I don't really a good water leg and I thought
67:08 caught you say that you go from and then substituting gas, but you
67:14 do the opposite, correct well you that if you can, but then
67:19 have no choice, but you have evaluate your logs pretty carefully.
67:24 Okay. Okay. Yeah. I like, how would you do
67:27 Like let's say like this was a . Well in a block where no
67:31 wells have been drilled and you saw amplitude anomalies and you wanted to see
67:37 you backtrack and see what the water response would be to see that those
67:41 . Okay. You can do that with great much greater care.
67:48 Okay. I mean, this is modern data. So I feel
67:50 you know, like you're going to good constraints on your physical parameters and
67:55 cord and took everything under the Nice. I'd be happy to look
67:59 that for you. Okay. Very good. Any other questions?
68:10 , thank
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