© Distribution of this video is restricted by its owner
Transcript ×
Auto highlight
Font-size
00:01 this conference will now be recorded. , Thank you very much.

00:08 3rd time for the record in composite modeling, mixing constituents, we could

00:15 wide bounds which are the void and pounds. They're the widest bounds tighter

00:20 are machines, Brickman and with specific , we can uh make an exact

00:28 um and when the end member properties close to each other, we're safer

00:35 a linear relationship. The wider those properties are the more different they are

00:41 each other. The more potential Garrity. Mhm. All right

00:50 what? What is a constituent? here we have a highly idealized

00:58 We have the matrix or the background material, which is the white.

01:07 then have added solid inclusions which are black and this was a scanned

01:15 So some of these are not so . So you can imagine some uh

01:19 ferocity inside the that solid material. then we've also added pore spaces which

01:26 are these circular objects And in this then the Yeah, dominant mineral is

01:37 background matrix. The secondary mineral is an inclusion that is embedded within that

01:46 . And the ferocity is also treated as the constituent either in a dry

01:55 , it's treated as air. And using the elastic properties of air and

02:01 of air or in a liquid filled or fluid filled rock. Uh could

02:08 a gas water mixture, whatever we the effective properties of the fluid in

02:14 course face. So the poor whatever they are, are explicitly treated

02:22 constituents. So this particular Rappe rock be what we would call a turn

02:30 mixture because we would have three The white matrix solid material, the

02:38 secondary mineral And the fluid in the space. So three constituents. So

02:46 one way to look at the And when we extend the uh wildly

02:53 average equation, for example, to minerals, that's what we did.

02:58 added up the travel time in each , the travel time and the fluid

03:04 the travel time in each of the . However, there is another way

03:08 look at the world uh instead of Iraq as having or the Iraq is

03:17 pour fluids as a explicit constituent, can treat the pore space and whatever

03:27 filling the pore space, we can it implicitly where instead of mixing zero

03:34 minerals and the pore filling material, can mix porous rocks. So we

03:44 the white rock which is porous. it has different properties now than the

03:51 mineral, but it's the properties of porous, a pure mono mineral lick

03:58 and we can mix that with inclusions porous material. So it's a different

04:04 of the world uh to the, know, obviously this may be very

04:11 in a certain situation where you have of one mineral embedded in another.

04:17 then again, if you have uh an inter penetrating pore space. It

04:23 be reasonable to think about things this where both solids, BB it white

04:29 black are in contact with and surround space. So this is what we

04:37 call a ferocity implicit model. as a first order approximation we could

04:45 the ferocity in both minerals is the . So the ferocity and the white

04:51 equals the ferocity and the black that's the first order approximation, but

04:57 not required to do that. You uh if you have a priori knowledge

05:03 some reason you think one mineral we may have more ferocity associated with

05:09 you could have different Torosidis. But the first order approximation, without any

05:14 information, we could just assume the is the same. So examples of

05:26 , explicit equations, we talked about time average equation where the total travel

05:32 is the sum of the travel times the individual constituent, individual minerals,

05:39 the volume fraction of that mineral plus coefficient times ferocity. And that

05:47 in the case of the wildly time equation is the fluid transit time.

05:52 in fact I could have crossed the . K. Ferocity out over here

05:57 I could just have treated poor fluid a constituent. Use the transit time

06:03 the poor fluid and the volume fraction the poor fluid is the ferocity.

06:07 the widely equation is very explicitly treating or the material in the ferocity treating

06:16 as a constituent. Uh We also the han equations uh coming out of

06:24 , um and you can do the thing by averaging velocity right now,

06:32 we saw a lot of different velocity relationships and anyone circumstance uh, widely

06:39 average equation form may work better or average may work better. I haven't

06:46 a compelling reason why one should use over the other. The widely time

06:52 equation equation was convenient when people were with sonic logs because sonic logs were

06:58 and units of transit time. So became a more popular use, But

07:04 not sure that there's ever been any of study deciding statistically which one tends

07:10 match ferocity data better. You could it either way. And in a

07:16 circumstance, one for may work better the other forms from. By the

07:24 , this forum is also in a lick. Rock was first introduced by

07:31 . So he said, the velocity a monumental alec rock is equal to

07:36 constant times ferocity plus an intercept. we'll refer to that as a hicks

07:44 and it's convenient to use. And we want to uh make the porosity

07:53 , if we want to remove ferocity these equations, remember these are the

07:58 fans of times or the mineral We can remove ferocity from the equations

08:06 just take uh the velocity average or average of porous rocks. So instead

08:15 course calcite and dolomite, we have limestone and dolomite rock. And so

08:23 for example, we could do a average. We could also do a

08:26 average. Um Later on we'll see uh this uh tends to give you

08:35 higher velocity for the composite uh than means of averaging. Remember we talked

08:42 reciprocal averages like with the Royce And later on we'll show that's doing

08:49 in between a linear average in a average of velocity seems to work pretty

08:56 . But anyway, in its simplest , you could do things this

09:00 So the X. I. And V. I. R. Now

09:04 the volume fraction and velocity of the mineral, the volume fraction of the

09:13 rock over the poorest rock constituents. so for each constituent then we could

09:21 a velocity ferocity relationship. We could anyone we want, it could be

09:26 dreamer and Gardner equation. It could the critical ferocity model. Uh It

09:31 be anything, it could be going Gardner's relations if these are unconsolidated

09:37 So uh it's immaterial. Uh you a velocity porosity relationship then, which

09:45 be with ology dependent which you now to here and then average those

09:52 Like I said, it doesn't have be a linear average. It could

09:56 something else that gives you a lower . Okay, so now which of

10:06 forms matches or measurements better porosity explicit prosperity implicit. And so here this

10:16 a database of a few 100 rock measurements. And it's uh velocity vp

10:25 top V. S on the bottom comparing for in Mexico pathologies and over

10:33 ferocity ease comparing predicted in actual And you see what happens is if

10:40 use a ferocity explicit model, notice limitation here. And the limitation is

10:48 the dependence on ferocity becomes mythology Right? The mythology goes into this

10:57 and it doesn't vary. The Prasit dependence doesn't vary with the mythology.

11:05 you can imagine if you had different poor shapes associated with different mythologies that

11:11 might you might have a different velocity relationship in different mythologies which we can

11:21 here. And so you can see that's exactly what happens if we compare

11:28 in actual velocities I measured in the . You see, it's it's

11:34 Uh it's not on the diagonal. And so there are biases. The

11:41 velocity rocks uh tend to, the tends to be too high, as

11:48 the do the high velocity rocks and intermediate velocities tend to be to

11:55 And same thing for V. And G. S. In

12:00 the standard deviation here is this is feet per second. So for bp

12:06 ft per second For v. It's at first glance is better 800

12:13 . But remember the shear wave velocities lower. So actually this is a

12:18 percent error. On the other if we use a process, the

12:24 model, we could remove these biases so now we're getting a nice linear

12:32 with, with a much better standard , much smaller prediction error. Now

12:43 could take the same approach and we uh try to predict shear wave velocity

12:51 p wave velocity. For example, it's suppose I'm trying to predict shear

12:59 velocity of the composite. I could in here the predicted shear wave velocity

13:05 any pure mineral. So instead of a porosity velocity relationship here, I

13:12 have a V. P. S relationship. So for example I

13:16 use the uh what tend to be nowadays the Greenberg and Castagna Relations which

13:23 gave you before uh you know, unit on the PBS rations.

13:27 So here beta share with velocity help P wave velocity and from different mythologies

13:37 have different coefficients. Uh huh. kind of funny that the equations we

13:44 were not our preferred equations. They equations which we were allowed to publish

13:51 a subset of the data we which was public domain data. So

13:56 were never allowed to publish the best that we had. But anyway,

14:02 is what's made it into the literature this is what most people use,

14:07 guess the the actual trends are still at BP if anybody because they acquired

14:14 company I was working for. I doubt if anybody is using those equations

14:21 , but people tend to be satisfied these equations. So what you do

14:26 you stick these equations in here and you can predict the velocity, but

14:34 than a simple average like this, in comparing to a lot of

14:40 uh we found that using a different was better and I'll show you that

14:45 a minute. Um so the idea is that xu wei velocity laws are

14:53 not available in the wells are old people that want to spend the money

14:58 acquire a sheer way blog. And uh if you have a few red

15:04 or you have a pseudo atomic, could be computed from the resistive Itty

15:10 neutron log or whatever, wherever you your p wave velocity log, if

15:15 have an idea of the lethality, then you could use V PBS trends

15:21 VP density trends and you could uh shear wave velocities. So in a

15:29 case you would bring conventional logs he would do a volumetric log

15:34 schedule mythology log, you have a p wave velocity log, you use

15:41 trend curves and you could predict a philosophy. Remember we never have pure

15:48 , pure limestone, pure dull but we can mix uh we make

15:55 predictions of the velocities, it eat the pure mythology. So from

16:00 we predict Bs in the pure mythologies then we do some kind of averaging

16:08 millet ology. So, again, a empirical from cause it medium

16:16 Okay, and this is the equation used, I mean in the simplest

16:21 you could ignore all ideologies and this better than pulling a number out of

16:26 air. You could use the mud line for example. But of course

16:31 going to be wrong if if you've clean sands or you've got lime stones

16:36 you have hydro carbons. Right? this might get you somewhere in the

16:40 but it won't be very precise and deviations from the mud rock line will

16:46 you very significant differences in seismic So we want to get more precise

16:52 that. And so here, uh equation looks complicated, but it's actually

16:58 simple. The X's are the volume , the alphas or the T wave

17:05 . And and so uh the alphas are the coefficients like the Greenberg and

17:11 coefficients. All right, so what do is for each mythology, we

17:20 the shear wave velocity for that Uh based on some of the

17:28 Uh well, basically using these trends . So this winds up being the

17:35 shear wave velocity And we do that we repeat that here except there's a

17:42 . So what we're doing here is similar to the hill average. We're

17:45 of cutting it and began the velocity in half. This would be the

17:52 kind of like avoid average and this be the softest kind of like a

17:57 average. It's not in module it's velocities but it's the same idea.

18:03 The answer is probably somewhere in between two. It could be on

18:07 it could be the other could be in between we don't know where.

18:11 we just average the two and that us again in the ballpark. And

18:17 that so we take the predicted Bs the D. P. V.

18:21 trend. Uh And we take a average a reciprocal average. We can

18:27 average those two, I should Yeah, linear volume weighted average,

18:33 reciprocal volume weighted average and half the . And that gives us our predicted

18:40 way philosophy. So if we don't hyper carbons, this is very simple

18:45 remember these V. PBS trends are bronze saturated rocks. Now this approach

18:52 work if you have hydrocarbons so you to do one better. And um

18:58 anyway, I'm brian saturated rocks. tested this on laboratory data. So

19:04 is predicted Bs versus observe. Es good prediction. Uh Here this is

19:13 a publication uh The original Greenberg and publication. This was all the laboratory

19:20 we had and so that was how did there and these were on what

19:26 saturated velocities. We also did the thing on airfield rocks and the prediction

19:36 was pretty good. Uh We have lot of success applying this to

19:42 And um actually the predictions sometimes seem defy belief. Right? So here

19:51 have a with ology log here, have the sauna cloth and vegetable sonic

19:58 and here we're comparing the predicted to measured shear wave lock. And you

20:04 see that they're right on top of other. That's why this algorithm has

20:09 so popular. Uh There are discrepancies where we have into betting and some

20:16 the thin layers and it's kind of . But at the time internally within

20:24 company we were working, a very friend of mine had inherited the sonic

20:32 research group. I had moved over another department. He had taken it

20:38 . We're still very close friends to day but it was a little bit

20:42 a competition because he was measuring the and I was coming along saying I

20:47 predict the logs and so uh it until we sat down and we decided

20:53 it's worthwhile to do both. That prediction is a good to see uh

20:59 the measurements and the measurements are necessary perfectly calibrate your prediction. And when

21:06 have discrepancies, that's an opportunity to something. Actually, it turned out

21:12 be very useful to be able to this. So a few things uh

21:19 out of this particular example and that when we used the gamma ray log

21:24 predict mythology, We have a lousy . Uh and our conclusion was that

21:31 mythology prediction was bad with the You have variable radioactive content in

21:40 You know, it's not just potassium story. Um it's uranium uh and

21:47 in your sands, you have radioactive . If it's an oil reservoir,

21:52 could have uranium precipitated in the pore . Uh If you have radioactive

21:59 uh if you have organic material which is associated with uranium, so the

22:07 ray log is very imperfect for estimating . Uh This was south texas.

22:17 decided that the neutron density log would a good way to estimate with ology

22:22 that's what was done here. And if we didn't iterate on the mythology

22:27 force to match, we just did with ology in a different way.

22:31 use the gamma ray log and we're to get a very perfect prediction.

22:37 calibration, This is using the global curves. That was what was most

22:43 about it. In fact, I so impressed with these results, then

22:48 was wondering why in these thin the prediction was actually going to lower

22:55 . Whereas the measurements seem to be off in those very thin layers and

23:02 are the shear wave logs, you have a means of estimating the quality

23:10 share wave laws because the velocities are very much the same way we measure

23:16 velocities. There's a semblance algorithm that at the similarity of wave forms and

23:23 the time lag where you have maximum . But the semblance value itself is

23:30 indication of how similar the way forms and the higher the semblance, the

23:36 your measurement is. So for this we went in and this is just

23:40 piece of the log. The log much longer, We had quite a

23:45 of statistics here, so we were to been the discrepancy between the

23:53 Right, So we look at the called error, let's just call it

23:57 discrepancy between the measurement and the It doesn't mean that the predictions wrong

24:03 that amount because there is experimental error the measurement. So, uh,

24:09 know, there's a discrepancy and if and if we plot below the standard

24:18 relative to the semblance. So we've all the values with high semblance,

24:24 know, so these are bins of and we measure the standard deviation of

24:31 discrepancy. And what we find a of one would mean you have identical

24:37 forms with identical amplitude, So you'll hit one. Uh but what you

24:44 is a definite trend as the semblance getting better, the discrepancy is getting

24:51 and you can then predict, you , where you're perfect, you

24:57 when you have perfect semblance what the would be. So that would be

25:03 best indication of your prediction error, what we also found was when you

25:09 very bad templars, you had really discrepancy and so I would argue.

25:17 where is this? This intercept would the prediction errors that were on the

25:22 of You know, 12 or something that, where the semblance is very

25:27 and you have very poor confidence in velocity measurement. We had a semblance

25:33 there around 30. So the point the discrepancy here we believe is more

25:39 error and the discrepancy here is more error. So anyway, quite a

25:46 prediction. And I would argue that these thin layers if we plotted the

25:51 , you would see that where things clipped here is you have low semblance

25:56 and and that's because of interferences. have actually is the seismic refracted wave

26:02 propagating every time you have an interface develop reflected and transmitted refracted waves and

26:11 get a complex interference pattern and you start your your way for him and

26:18 velocity measurements not very good. Just example. These were actually paleozoic shells

26:30 . And quite a good prediction Uh and here was the cross plot

26:37 predicted uh birth is measured. These off door die paul measurements and uh

26:49 was back in the early 90s by were just becoming popular and uh so

26:56 flooding the predicted shear wave velocity against measured shear wave velocity. This came

27:02 the scientific publications that we have to , you know, M.

27:06 S. Units. Um Overall pretty high correlation coefficient .9 uh various 32

27:18 for kilometer. Okay, so uh is in transit time but you can

27:25 that that's a pretty small error in time. And what was interesting is

27:34 this particular? Well we had two typos tools run two different shareware vlogs

27:41 so we said, how well do agree with each other? And what

27:46 found was that the measurements, The was only .87. Where is the

27:54 the court to one of the The correlation was .9. And why

28:00 would it be worked? Why would measurements repeat measurements be worse? And

28:06 we tried to correct for variable depth stretch but maybe we didn't correct it

28:14 . So you know, you your depth registration is not always exactly

28:20 but we did try our best to that. So the results are comparable

28:30 another example and this this is showing well how in thin layers the direct

28:36 tend to go bad. Right? so the line is the prediction and

28:42 is in there. That was A variety of applications came out of

28:50 are drilling engineering group was very you know, they needed to measure

29:00 ratio for hydraulic fracturing design and this a really interesting case. This was

29:06 North Sea blow out well and uh was a litigation basically with the british

29:18 , we wanted to drill a relief , it was a lot like what

29:21 with the deepwater horizon. But this in the North Sea and we had

29:25 convince the british government to let us a relief well. Whereas uh with

29:31 deepwater horizon it was the government was to be convinced as to a remedy

29:38 they let the fluids flow the oil for months before they allowed BP to

29:45 what BP needed to do to to the well in. But anyway,

29:51 was in the North Sea and to the government, we have to show

29:55 that we could predict the closure And so here we have uh the

30:03 poor pressure the by the way this after logging. Right? So we

30:08 the pore pressure, we have the drilling mud pressure which is slightly above

30:16 pore pressure, which is what you . Uh We have the calculated horizontal

30:24 and this is from the log. you need persistence ratio and you need

30:31 what we consider proprietary algorithms to predict closure stress. There's, there's a

30:38 slumber J equation that people use, not what we use. But uh

30:44 then these were the leak off These are the measured closure stresses and

30:49 can see we pretty well nailed it those slightly more permeable units there.

30:58 so we were able to convince the that we knew what we were

31:03 And we could drill the relief wells that's because we had of persons ratio

31:09 , which had not been measured, which we calculated using these techniques.

31:19 . But things get complicated when you hydro carpets. Uh We said it's

31:27 a simple averaging equation From VPBS trends were are for 100% brine saturated

31:36 But what do you do if the saturation is not one, you don't

31:43 the trend curve to use. So this is what we assume we

31:48 coming in, we have p wave , ferocity, water saturation, the

31:54 and fluid fractions and properties and the . And the way the algorithm that

32:02 is we take an initial guess at the p wave velocity would be if

32:09 water saturation was one that doesn't have be a very precise gas. Uh

32:15 uh well, iterating until we get the right answer, but uh if

32:20 in the ballpark things will converge Right? So, well, guess

32:25 the p wave velocity would have had we had 100% brine saturated

32:30 And in that case then if W equals one, we could use

32:37 B. P. B. Trends and we could use the mixing

32:42 and we could then predict the shear velocity what the shear wave velocity would

32:47 been, had the formation had a saturation of one from that and from

32:56 from the density, we will then be able to, and prosperity will

33:02 able to compute what the bulk and modules are. And those are probably

33:08 because our shear wave velocity is probably until we converge to the right

33:14 But let's let's run with them, what we get. Uh we uh

33:21 the dry frame properties knowing that is wrong. But then, given that

33:30 know we have the measured sw, think we know what the fluid properties

33:34 from the battle and wang equations. we could uh then uh at the

33:40 water saturation, we could go the way and we could predict the p

33:45 philosophy. And if our initial guest right, then we'll predict the p

33:51 velocity correctly. If the original guest wrong, then our predicted VP will

33:59 match the measured VP. And so go back and iterate. Or you

34:04 do steep newton, steepest descent or kind of optimization algorithm you want.

34:10 and you could uh you could repeat process until your predicted vP matches the

34:18 vP. Uh So in the output this process, we get two

34:25 we get the shear wave velocity at institute saturation. So that's the what

34:32 measured shear wave velocity would have been , we had the log And we

34:37 get the p wave velocity at award of one. Uh We could uh

34:44 this in the other direction. If starting with water saturation equal one we

34:50 then compute V. S and P at a new water saturation because

34:55 the drive, once we've got the module list and we could produce an

35:01 at any saturation we want. And so in the paper, this was

35:10 flow chart for the algorithm and uh was going to try to take you

35:14 it, but I found that this a much clearer way to present

35:19 But but just for uh the record is the flow chart for the algorithm

35:27 the Greenberg and Castagna 1992 paper. , so uh again, for historical

35:39 , we do this uh back, know, if you ever heard of

35:43 company called Arco, we were all for our co at the time we

35:48 this and this was an example of print out of the program at a

35:55 death. Right? And so you your inputs, you have your measured

36:02 saturation, you also have the desired statue saturation. So the water saturation

36:09 which you'd like to do the So now we could do not only

36:13 wave velocity prediction, but we could fluid substitution. And of course you

36:18 to know the ferocity now and then predict the velocity density and shear wave

36:27 at the desired new water saturation. uh we could use this for fluid

36:37 . And so here is an example we flew substituted in this range here

36:43 this interval and we put different fluids we had gas live oil, dead

36:50 . This was the p wave velocity . Of course the shear wave velocity

36:54 not going to change very much with fluid as we learned in the last

37:02 are one of the driving forces for this was being able to model offset

37:11 so we can model the HBO the variation with offset. And so uh

37:18 had a synthetic wave propagation program and it to actual gathers. And what

37:25 found was that our predictions were agreeing the data. Right? So um

37:32 solid curve here is the predicted a from from the synthetic gather and uh

37:41 data points here are from the real and the dash line is the fit

37:48 . I'm sorry. It's the other around the dash line is the prediction

37:51 it goes all the way to zero incidents. And the black line is

37:56 fit a statistical fit to the data presumably that scatter is noise lot of

38:08 . Um This was a gas reservoir the way, this was a shallow

38:14 reservoir. It was an amplitude increased offset. Uh This was another gas

38:20 above an oil reservoir and it was interesting case. Uh of course in

38:25 gas reservoir were predicting a very low . PBS ratio and we're matching the

38:31 essentially perfectly. The oil reservoir was . It was a low G.

38:37 . R. And in the oil were actually predicting a higher V.

38:43 . V. S. Ratio. And that's because it was a very

38:46 sand and the shells were relatively hard hard. So the shells actually were

38:55 the PBS ratio than the oil filled . And that produced a relatively

39:01 Yeah. Now as I mentioned where you have a discrepancy, uh

39:09 uh it's an opportunity to try to why you have the discrepancy. So

39:15 we have a with ology log here have our V. P.

39:18 S. Log which by the way sheer wave transit time divided by p

39:22 transit time. That is the P. B. S ratio.

39:26 here was the measured shear wave transit . So slow as to the right

39:39 If you do this, assuming the saturation of one, then you you

39:45 be able to find discrepancies that are with gas and what will happen,

39:51 you're predicted shear wave velocity will be low because you're assuming your brine

39:56 you're predicting hi V. P. . S ratio. So given a

40:02 VP, you'll predict a high P. V. S. And

40:06 predicted Bs will be too low and could be in the indicative of

40:11 especially if you have low resistive, wet. Hey it might be a

40:15 of recognizing that this was an interesting because we didn't have a shear wave

40:29 in this case. What we had the P wave sonic log. And

40:33 we had a very finely sampled This was before in these relatively shallow

40:42 , relatively low velocities. See these high transit times. We in the

40:49 days we didn't have reliable sherwood So, uh what we have then

40:58 our predicted be PBS ratio, which the solid curve. And we're comparing

41:04 to the VSP measured ves. So is kind of, you know,

41:09 think like a kind of a mud line prediction. And it agrees pretty

41:14 with the DSP, some problems in , but maybe we didn't have the

41:18 quite right. But then we had serious deviation. If we continue assuming

41:25 saturation, we're predicting a higher PBS ratio. A slower shear wave

41:31 time. And the VSP bears Right. And what we find is

41:40 we have to use a Mhm. gas that trade if we use the

41:46 saturated logged and or assume that the for gas saturated, we would predict

41:55 velocities here. And what you can is that the BSP is either measuring

42:03 close to our predicted gas that traded here and here, we're somewhere in

42:09 gas and brine suggesting that there's gas the section someplace. All right.

42:16 we have limited resolution and this was fairly large interval here. So,

42:24 not suggesting that we have 1000 ft pay Or more. What is

42:29 21,500 ft of pay. We're not that what we're suggesting, uh,

42:35 gas in the system so we might in some kind of micro slippage

42:51 Um Also remember we if we have and S wave velocity is predicted,

42:56 could then calculate elastic module I and are used for engineering applications. This

43:04 on the north slope of Alaska. was a limestone reservoir there, the

43:10 formation. And we had a pretty predictions of share module lists in bulk

43:21 . Okay. There's a lot more can talk about and uh, I

43:30 think I want I want to I it's too much and so I'm going

43:36 cut things short today, so I'm here. Um, are there any

43:44 then? So yeah, I this is all your notes go there

43:52 a lot more slides here, but think it's it's more than I want

43:57 to have to worry about. even though they're in your notes,

44:01 won't be on the test. So at this point. Okay. Any

44:09 ? Yes,

-
+