| 00:01 | this conference will now be recorded. may recall this was a this start |
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| 00:10 | by the way it came from Gregory . That's in your reading list in |
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| 00:16 | you want to read more about, prepares the static and dynamic Young's module |
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| 00:24 | . Remember Young's module is is a of balkan sheer module lists. And |
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| 00:31 | for an unconfined rod basically, or unconfined cylinder. And it's the the |
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| 00:42 | between uni axial stress and uni axial . Or you could think of that |
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| 00:48 | longitudinal stress and strain. So basically I squeeze on the ends of |
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| 00:55 | what's its fractional change in length. for most of these rocks, these |
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| 01:03 | compare the static and the dynamic module . So the white bar is the |
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| 01:09 | module lists. And the dynamic module is bigger than the static module lists |
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| 01:16 | most cases. And we understood this two reasons have the two major differences |
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| 01:24 | static and dynamic module I our dynamic I come from wave propagation. So |
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| 01:32 | an Osceola Tory stress and it's a small stress. It's a small devia |
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| 01:40 | stress. So small stress corresponds to strained. So you're not deforming the |
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| 01:49 | very much and you're also deforming it a high frequency, which means if |
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| 01:58 | any dispersion for body waves as opposed surface waves. You may have learned |
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| 02:04 | surface wave dispersion where the low frequencies faster. On the other hand, |
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| 02:10 | body waves, the high frequencies are . So both because of strain amplitude |
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| 02:18 | small, in frequency being high, not pushing the strength of different contact |
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| 02:29 | or different pores in the rock? therefore the rock acts stronger, It |
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| 02:35 | less deform a ble. And so have a larger Young's module lists. |
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| 02:42 | most of the time. However, was one rock and so you can |
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| 02:49 | this as a charity limestone. There is a I don't know if |
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| 02:54 | ever seen these things, but there be church modules in the limestone. |
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| 03:01 | and in for that rock, the module list was bigger than the dynamic |
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| 03:09 | . So how can that be? got much bigger strain amplitudes and you're |
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| 03:15 | low frequency, it's a it's a compression, right? So it's a |
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| 03:21 | change in volume, it's not the change in volume or length in this |
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| 03:26 | , not the tiny change in length you would get from passing away through |
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| 03:32 | . It's observable and it's zero It's static, you apply the load |
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| 03:38 | you hold it there and yet the module, This is bigger than the |
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| 03:44 | modules. How can that be? I've asked for a hypothesis. I've |
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| 03:49 | asked for you to prove it. have not asked for the right |
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| 03:54 | I've just asked for a physical guess to some conceptual model for why this |
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| 04:03 | be happening and so far I've gotten from anybody. So I wanted to |
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| 04:10 | you a little bit of a And let me ask you the |
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| 04:15 | what happens if I have a cracked where I have very fine cracks with |
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| 04:22 | apertures? And what happens if the amplitude is greater than the crack |
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| 04:30 | Okay, so, I'm going to that question and think about what the |
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| 04:35 | of that would be. And then about the difference between a measurement with |
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| 04:41 | very tiny strain amplitude as compared to measurement with a large strain amplitude. |
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| 04:48 | , that's a clue. I hope picks up on that. And while |
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| 04:54 | was looking at this chart, I that I had neglected to point out |
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| 05:01 | very interesting thing. And that is softer rocks tend to have higher ratios |
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| 05:09 | the static and dynamic. So, for the soft rocks, the dynamic |
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| 05:16 | was much bigger than the static module and that seemed to be less so |
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| 05:25 | the stronger or higher velocity harder So, um does anybody want to |
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| 05:36 | a hypothesis as to why why would rocks have a bigger difference between dynamic |
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| 05:44 | static module lists? At least percentage ? I mean, it has something |
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| 05:56 | do with the frequency dependence. Uh Well, it could, I'm |
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| 06:02 | asking for a hypothesis. Again, not asking for a reason, but |
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| 06:06 | a conceptual model. So, if could conceptually uh hypothesis why a frequency |
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| 06:14 | would uh create this difference in I'd be happy to entertain that. |
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| 06:22 | the other side of the coin is amplitude? Uh So what about straight |
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| 06:30 | ? Might be very different or how a soft rock, react differently at |
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| 06:36 | strain amplitudes compared to small strain amplitudes back to your stress strain curves. |
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| 06:51 | what happens if we have a very change in stress? What happens is |
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| 06:58 | keep increasing the change in stress? , rupture. What what happens before |
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| 07:09 | get to rupture? What you plastic deformation, plastic deformation. |
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| 07:17 | suppose we were measuring the relationship between and strain. And suppose we we |
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| 07:26 | when we passed the elastic limit, flatten that stress versus strain curves. |
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| 07:33 | ? So, suppose in my measurement the elastic module lists, suppose I |
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| 07:41 | the range of the elastic field, I go into the plastic field. |
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| 07:47 | will happen to my measured module Remember the measured module is is the |
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| 07:55 | divided by the strength. So, that curves flattens for a given change |
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| 07:59 | stress, don't I have a bigger in strain? I think I asked |
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| 08:15 | question. So, what does that to the elastic module is suppose I |
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| 08:22 | my delta stress? Suppose I exceed elastic limit. How is that going |
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| 08:29 | change the elastic module lists? As to not having exceeded the elastic |
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| 08:44 | You can have a lot more stress for a longer period of time before |
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| 08:51 | happen happens. Okay, so, trying to measure the elastic module is |
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| 08:57 | . So what is the elastic module ? It's the strain versus the |
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| 09:07 | Right? It's the stress divided by strain. And now uh I have |
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| 09:14 | big change of stress. If I the elastic limit, is that going |
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| 09:19 | give me a bigger or smaller change strength immediate? It's a bigger change |
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| 09:36 | strain, right? Because it's a curve, right, stresses the vertical |
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| 09:40 | , strain is the horizontal axis that bends, it goes flat when you're |
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| 09:46 | the plastic field for a given increment stress, you're having a lot more |
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| 09:53 | . And if stress overstrained is your module lists if I'm spanning from the |
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| 10:01 | field into the plastic field at I wind up measuring a smaller ratio |
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| 10:09 | stress to strain. Do you see if I had stayed completely in the |
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| 10:14 | field, I would have had a curve, Right? And the slope |
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| 10:19 | that curve is the elastic module is if my if I have extended into |
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| 10:25 | plastic field, I now have a stress for a smaller slope doughnut. |
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| 10:34 | with me on that. So, if the static measurement is a is |
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| 10:40 | large measurable change or a large change stress Such that I have a measurable |
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| 10:48 | in length, isn't it? Isn't possible that I've gone into the plastic |
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| 10:55 | and wouldn't that be more likely in soft rock, write a soft rock |
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| 11:00 | gonna go to uh the elastic limit going to be at a lot smaller |
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| 11:07 | than in a hard rock. You my point? Yes, yes. |
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| 11:15 | . But to follow up on that , why are the limestone is kind |
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| 11:17 | plotting in the middle? Because we expect them not to plastic lee to |
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| 11:22 | . We would expect them to have very small plastic realm and just brutally |
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| 11:26 | form almost immediately. Yeah, that the interesting thing. Um you |
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| 11:31 | lime stones do have a relatively high ratio. In fact, there are |
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| 11:36 | lot less brittle than courts, courts is much more brittle than calcite. |
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| 11:46 | , okay. Yeah. And keep mind that some of these are poorest |
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| 11:50 | steps to Alrighty, okay, now were some questions about this one and |
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| 12:00 | do have a question on the brittleness um you said suspicious materials versus |
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| 12:07 | It's then why in the for you know, like on the, |
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| 12:13 | the Permian basin, especially along the margins, are you getting these like |
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| 12:18 | , really amazing production these really awesome versus in the Eagle ford or the |
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| 12:26 | ? I'm just curious like from a mechanical standpoint, yeah. You |
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| 12:32 | keep in mind everything is relative, ? So, you know what is |
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| 12:36 | it and my understanding is in the for the more salacious zones, |
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| 12:41 | better and the same thing in the . Right? So, uh, |
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| 12:48 | know, a salacious limestone would be brittle than a porous limestone? For |
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| 12:57 | , clean porous limestone. It it just seems odd like the production |
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| 13:02 | that you get and you know, areas that are highly car, you |
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| 13:08 | , highly limestone with really not that salacious and you're getting these absurd production |
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| 13:15 | versus, you know, and your for it. Even if you have |
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| 13:18 | solid, suspicious, uh, you , solid salacious materials after a |
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| 13:23 | year and a half. I your production just absolutely shoots down. |
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| 13:29 | I was just curious if you had insight on that. You know, |
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| 13:33 | don't, other than that, there a lot of geological variables. It's |
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| 13:37 | only the brittleness that matters, There's, there's more to it than |
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| 13:43 | . So, you know, what the matrix porosity? What is the |
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| 13:48 | , What, you know, what of permeability is do you wind up |
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| 13:53 | ? What kind of fracture pattern do have? Uh, they're, they're |
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| 13:57 | , there's a lot going on. I can't give you a simple answer |
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| 14:06 | you, uh, is the why is there more production in the |
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| 14:10 | than in the Eagle? 3rd? that the question? I mean, |
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| 14:14 | guess it just seems odd with, know, because we're everyone's taught suspicious |
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| 14:20 | . I mean, delicious. That's you look for in order to do |
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| 14:25 | unconventional. And it's just kind it seems like the Permian is kind |
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| 14:30 | proving that a little, it's, know, maybe a little wrong or |
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| 14:35 | , you know, it's an Let me keep, let me just |
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| 14:39 | it this way. It's the stratification Hassan's ratio that determines your fracture |
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| 14:46 | Right? So a lot of it to do a lot of it is |
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| 14:51 | , you know, relative to the layers. And how far can you |
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| 14:56 | a fracture before you go into an ? For example, how continuous is |
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| 15:03 | compartment that you're in because it gets dangerous if you're near false and those |
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| 15:10 | are conduits for water. There's just lot going on other than just the |
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| 15:16 | . The absolute brittleness of the material . Mhm. Yeah. So uh |
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| 15:23 | guessing that yes, yes, a a court site is going to be |
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| 15:30 | more brittle than the limestone. And a salacious limestone is going to |
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| 15:35 | more brittle than a clean calcite But there are many other geological variables |
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| 15:43 | impact the production. Okay, that's very diplomatic way of saying, I |
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| 15:51 | know. I can't give you the answer as to why the Permian is |
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| 15:55 | productive than some other areas. Um don't know enough about that basin to |
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| 16:01 | understand why it's so productive other than are a lot of hydrocarbons there. |
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| 16:09 | , okay. Um next exercise that saw people having trouble with and this |
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| 16:16 | partially my fault because I gave you many trivially easy questions just because I |
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| 16:23 | you to get familiar with the I didn't give you many that work |
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| 16:29 | any computational difficulty associated with with This had very slight computational difficulty, |
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| 16:38 | I saw a lot of people struggling it. And um I asked you |
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| 16:43 | plot density, average density, pressure gradients, et cetera versus |
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| 16:50 | And one of the keys was I you to plot density versus death, |
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| 16:55 | I also asked you to plot average vs death. So what's the |
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| 17:02 | Well the density versus death, you the equations right here. So zia's |
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| 17:09 | ? It's just a matter of plotting density. But what is the average |
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| 17:13 | versus death? That's at any The sum of all the densities above |
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| 17:19 | divided by the number of data So divided by the number of |
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| 17:24 | So that means what you have to is you have to integrate these |
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| 17:28 | you could do it numerically by taking running some of all the values above |
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| 17:33 | . So at any depth you take thumb of all the densities above you |
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| 17:37 | then divide by the number of data . All right. So um so |
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| 17:43 | the key. And of course the depends on the average density above |
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| 17:52 | Uh And that's how you would get pressure gradients. Then. There's this |
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| 18:03 | nasty little guy um This was a weeks ago and I said, well |
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| 18:08 | look into it. Well, I'm man of my word and I decided |
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| 18:13 | look at this plot. I've blown up. It was one of map |
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| 18:17 | examples from his course notes. And uh it was pointed out that this |
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| 18:26 | unrealistic and I was asked to explain and I should have known the |
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| 18:33 | but I was on the spot and was struggling and I couldn't figure out |
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| 18:37 | answer on the spot. In we're going to cover material today or |
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| 18:43 | this unit. I don't know if get to it today, but we'll |
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| 18:47 | uh an explanation for what's going on . and uh there are few clues |
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| 18:55 | to what's going on. Number one you look at the dry rocks, |
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| 19:00 | no difference between the dry and saturated . So how can that be? |
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| 19:06 | can there be no difference? that must mean the porosity is very |
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| 19:11 | . If the porosity weren't very you would see a density effect and |
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| 19:15 | saturated velocities would be slower than the velocities. So they're right on top |
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| 19:21 | each other. So we can conclude porosity is low enough such that we |
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| 19:26 | they don't have a significant impact on density. So, I mean, |
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| 19:31 | the velocity also, Well then, the big change of velocity with |
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| 19:38 | If the porosity is so low. this implies that we've got a lot |
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| 19:43 | very flat pores, probably fractures or fractures. There are enough of them |
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| 19:51 | affect the velocities significantly, but not many to give you a significant |
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| 19:59 | So, you know, you could a huge number of very flat microfractures |
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| 20:06 | an insignificant ferocity of less than a . So I'm concluding that we have |
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| 20:15 | we have a big change of velocity . I'm concluding that we have a |
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| 20:20 | of low aspect ratio pores and the that dry and saturated are the same |
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| 20:26 | that the total porosity is not very . Now, I'm also now, |
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| 20:33 | also have to assume something else about pores for the sheer velocity not to |
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| 20:41 | affected for this saturated shear velocity, to be effective. I can't have |
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| 20:47 | situation where different pores are compressing two amounts or sharing two different amounts. |
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| 20:56 | different pores are volumetric lee deforming two amounts because if that if that were |
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| 21:06 | then my shear wave velocity would be for the saturated rock as for the |
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| 21:13 | . So, how can that Well, suppose I had oriented micro |
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| 21:19 | , suppose they were all in the direction. Could if they were fully |
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| 21:28 | saturated, you could you could see the shear waves would preferentially if they're |
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| 21:38 | in a particular direction, then the wave as it shears, the rockets |
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| 21:44 | to try to close those pores and those pores are disconnected, then the |
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| 21:52 | in the poor is going to resist closing of that poor, which means |
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| 21:58 | the rigidity of Iraq is going to on whether you have fluid and the |
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| 22:02 | or not. The the poor, oriented low aspect ratio pour with fluids |
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| 22:12 | it will resist sharing. Right? you're trying to the sharing is trying |
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| 22:17 | compress that poor is trying to close poor and that poor won't close or |
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| 22:23 | or the fluid it's pressure will increase you try to close that poor, |
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| 22:28 | going to be resisting that compression so it will increase your rigidity. But |
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| 22:36 | don't happen. We don't have that unless its poorest enough such that the |
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| 22:42 | effect is canceling that out. So could be happening. That would be |
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| 22:49 | coincidental for it to perfectly cancel like . So either so it implies that |
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| 22:58 | microfractures can't be disconnected or on the hand, it could mean an |
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| 23:06 | a tropic distribution of these fractures so the closing of one fracture is compensated |
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| 23:15 | the opening of another fracture. So the if the fractures are randomly oriented |
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| 23:21 | it's possible that even if they are with fluid in them um you would |
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| 23:29 | no difference in rigidity now. Uh ? Uh let's see. Okay. |
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| 23:36 | had a thought if okay, I'll back to that. I I had |
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| 23:43 | profoundly important thought but but I lost . Okay now let's move to the |
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| 23:49 | all wave velocity. We've already decided if there is a big change in |
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| 23:57 | in the dry rock, that must a lot of cracks or micro |
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| 24:05 | And you notice that at low the smaller pores or the lower aspect |
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| 24:11 | forest will close for first and then we increase the pressure, more and |
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| 24:17 | , higher aspect ratio pores will So this gradual changes, suggesting a |
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| 24:25 | distribution of aspect ratios. If all cracks were very, very, very |
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| 24:30 | low aspect ratio, you would have a more precipitous change with pressure. |
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| 24:36 | the fact that it's a continuous drawn change suppose uh suggests micro fractures with |
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| 24:43 | wide variety of aspect rations. Uh we've already decided that there are a |
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| 24:50 | number of cracks and why this big , where we've already concluded it's a |
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| 24:59 | porosity rock and yet the p wave . And we've concluded it's got lots |
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| 25:06 | fractures and yet the p wave velocity not very dependent on the on the |
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| 25:14 | . And so what must be Okay, I just remembered my very |
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| 25:19 | point. What must be happening here a these are these pores filled with |
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| 25:28 | when you fill these cracks with it makes the rock much less |
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| 25:34 | Um And in fact, I'll show theoretical equations that kind of proves my |
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| 25:42 | when we do gasman fluid substitution, show you that it's a little bit |
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| 25:49 | , but the lower the porosity. you if if you have a lot |
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| 25:54 | cracks, the bigger the fluid substitution , the bigger the effect of going |
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| 26:00 | dry to wet it is counterintuitive, I'll show you in the equations where |
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| 26:07 | happens. Um Now, the other I had was, how could |
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| 26:15 | how could I'm suggesting that these pores not in communication with each other? |
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| 26:22 | do we fill them up? How did we get them filled with |
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| 26:27 | ? And the important distinction is when say disconnected in this sense, I |
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| 26:33 | , acoustically disconnected for the time period the frequency of the seismic or of |
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| 26:40 | acoustic wave. These are ultrasonic In these laboratory measurements the pores might |
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| 26:47 | well be disconnected, but you could , if you take a lot of |
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| 26:51 | to saturate it, you could statically those pores. All right, so |
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| 26:58 | are effectively disconnected. All right. I hopelessly confuse everybody by the |
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| 27:06 | There are a couple of papers, found the paperwork that these original measurements |
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| 27:12 | from and this is ZW wang. It's in a somewhat obscure journal. |
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| 27:20 | and I don't actually have the original , but I found the reference, |
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| 27:24 | also a paper in the leading edge you can find pretty easily. It's |
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| 27:30 | ZW on its H Wong Who is well known rock physicist in uh in |
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| 27:38 | . And what he showed was that could reproduce this behavior using Custer toxins |
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| 27:46 | of the kind that we've already done . Um And so theoretically we can |
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| 27:55 | this happen whether or not it's realistic another issue, but we can observe |
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| 28:02 | in the laboratory and we could theoretically it happen. Did that answer the |
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| 28:10 | by any chance? I think I think I followed. But the |
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| 28:14 | question that you did say was in disconnected at ultrasonic. Yeah. So |
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| 28:22 | next question is, what about logging seismic frequencies? Can we still make |
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| 28:27 | assumption or not? Right, That is a huge, huge |
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| 28:34 | Uh generally uh seismic you have a more time and uh you're it's more |
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| 28:42 | things are more likely To follow the be very close to the zero frequency |
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| 28:51 | . The real unknown is sonic and sonic. I'm going to give you |
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| 28:56 | terrible answer which is sometimes you see sometimes now ah given the rock |
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| 29:03 | there are various models which by the , I mean theoretical models for wave |
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| 29:09 | through a porous medium. There are number of different models. None of |
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| 29:14 | models agree. But some of the in some rocks could give you what |
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| 29:19 | called a characteristic frequency below the sonic . And some people. And some |
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| 29:27 | will put it above the sonic And of course that depends on the |
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| 29:32 | . Right? So some formations the log is in the high frequency regime |
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| 29:38 | some work formations in some some theoretical . The sonic logs are in the |
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| 29:43 | frequency regime. We do know from shot corrections that sonic logs tend to |
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| 29:50 | a few percent faster than seismic Uh So in most of the strata |
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| 29:58 | section, we think the sonic logs closer to the laboratory velocities. |
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| 30:06 | there is one important uh ah exception that is porous reservoir rocks. So |
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| 30:16 | sMA originally um ah showed that in gas sandstone reservoirs that you're more at |
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| 30:27 | at the seismic end. Uh So , uh this is a question that |
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| 30:34 | not have a very clean answer. I'm sorry to say. Yeah, |
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| 30:40 | , I think I follow it and makes sense but I'm gonna have to |
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| 30:43 | on that one, but I appreciate the answer. Thank you. It |
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| 30:49 | it was an informed answer, but I I agree. Not a very |
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| 30:53 | answer. Okay, so then this another one I was struggling with. |
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| 31:01 | I'm I've only been looking at this for 25 years now and there's something |
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| 31:09 | teaching online that made me look at differently. And as as I was |
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| 31:13 | it to you, I was having kinds of thoughts and getting lost uh |
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| 31:19 | looking at the data. And I mention the key to understanding this these |
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| 31:28 | . I don't know if anybody picked on it, but I said these |
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| 31:31 | felt sympathetic sand stones. I just to remember that. And as we'll |
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| 31:37 | fell Spars act very differently from Right? If you remember our discussions |
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| 31:47 | uh V. P. B. ratios in dry sand stones. I |
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| 31:51 | emphasizing clean courts sand stones, And I said at the low velocity |
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| 32:01 | , ah you can understand their P. B. S ratio by |
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| 32:06 | sphere pack. V. PBS I showed you that dry sphere packs |
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| 32:10 | very low V. PBS ratios irrespective the distance ratio of the grains. |
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| 32:19 | the other hand, we thought we about taking minerals and adding inclusions to |
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| 32:25 | mineral. And in the case of , courts itself has the same |
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| 32:31 | P. P. S ratio as sphere pack. And so you don't |
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| 32:36 | a big change in the dr P. V. S ratio as |
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| 32:40 | span the porosity regime from a loose of grains to a cracked solid with |
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| 32:48 | space inclusions in it. Right? PBS was always 1.5. And I |
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| 32:54 | mention that if you were in a , that would have to change as |
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| 32:59 | went to uh more towards the Solid side, you would have to |
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| 33:04 | to a higher V. P. . S. Ratio for the dry |
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| 33:08 | as opposed for, you know, plastic limestone. Uh you would be |
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| 33:15 | likely to approach a lower V. . B. S. B. |
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| 33:19 | . V. S ratio. Like sphere pack. Okay, so uh |
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| 33:23 | turns out that uh fell Spars also hell calcite had the mineral itself has |
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| 33:29 | high V. P. V. ratio. So if you look at |
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| 33:33 | particular rock, okay, it's a . Uh it's very felt specific. |
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| 33:38 | are like clustering sediments in china they're very immature. So think of |
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| 33:47 | as being our Kosik, a lot feldspar associated. And here we're seeing |
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| 33:56 | same rock frame. So it's not the packing is changing. But when |
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| 34:02 | go to very low pressure, it's like a loose aggregate, a looser |
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| 34:08 | of grains. We have a P. B. S ratio for |
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| 34:10 | dry rocks of 1.53. and I've Loosely picked that off of uh of |
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| 34:18 | graph, I may be slightly Right? And it was just a |
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| 34:21 | look. And I came up with numbers, I came up with |
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| 34:27 | You pressure it up and what are going to do to these grains? |
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| 34:30 | going to push them more closely against other and instead of point contacts between |
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| 34:36 | grains, you're going to flatten those as you jack up the pressure. |
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| 34:43 | so what happens is we find an in the dry rock, The PVS |
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| 34:49 | , it's increasing like it would if weren't dealing with courts. So I'm |
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| 34:57 | that what we're seeing is a deformation the grains such that they are acting |
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| 35:02 | like a sphere pack here and they're more of the influence of the grain |
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| 35:09 | . PBS ratio at the higher Um So some other conclusions we |
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| 35:18 | we could conclude that this rock is because I have an observable drop in |
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| 35:25 | shear wave velocity as I go from or air saturated to brian saturate. |
|
| 35:33 | So it's porous and I see a fluid effect as I increase the |
|
| 35:40 | Um I'm suggesting that that's because the frame is becoming stronger and stronger, |
|
| 35:47 | that it needs less and less help the fluid to resist the compression. |
|
| 35:55 | I think I understand what's going on . Any questions on this guy? |
|
| 36:06 | It also seems to suggest that I'm an observable change in the porosity here |
|
| 36:12 | I increase the pressure. So that mean a lot of uh defamation of |
|
| 36:18 | or re compaction of the grains so to reduce the porosity as you jack |
|
| 36:24 | the pressure. Okay, so this us back to gas mains equations and |
|
| 36:33 | kind of rushed through this last time uh we need to look at this |
|
| 36:39 | carefully. These are incredibly important equations uh the gasman equations at least are |
|
| 36:49 | one of the few theoretical equations that believe works right? And so, |
|
| 36:58 | the reason it works is gas mains are not trying to build the rock |
|
| 37:05 | scratch right? If I'm going to build Iraq from its constituents, I |
|
| 37:13 | to have taken into account in great all kinds of microscopic things that are |
|
| 37:21 | on in a very small scale and a scale that I can't usually characteristic |
|
| 37:26 | cleanly and in the end, even I was able to do a poor |
|
| 37:32 | to to a very fine level, there are things happening at these point |
|
| 37:39 | that, you know, we just don't know how to characterize really |
|
| 37:44 | Uh and then I would have a problem uh of simulation. It would |
|
| 37:49 | a big simulation actually. Um and in the end, what, what |
|
| 37:55 | I really have learned? Um it out that people have claimed good success |
|
| 38:02 | this in predicting permeability, for doing a poor scan and uh from |
|
| 38:09 | uh apertures or the the distances from side to another side of a poor |
|
| 38:18 | . Being able to calculate numerically the permeability you would get from the poor |
|
| 38:25 | simulating passing fluid through it. And has been some reasonable success in doing |
|
| 38:33 | , but I don't know anybody that's , claims success in being able to |
|
| 38:37 | that with velocities or for that elastic module. And so most of |
|
| 38:46 | theories are way over simplified in order be able to get a mathematical handle |
|
| 38:53 | things to get our arms around We we have to make oversimplified assumptions |
|
| 38:59 | penny shaped cracks, right, ellipse lips, idol inclusions in Iraq or |
|
| 39:05 | uniform spheres in a particular arrangement. are all highly idealized theoretical situations and |
|
| 39:13 | good for understanding conceptually what's happening, they're very bad at predicting precisely what |
|
| 39:22 | the answer is going to be. the other hand, gas mains equations |
|
| 39:28 | try to build the rock from All the all gas mains equations do |
|
| 39:34 | tell you for a given rock with rock frame with whatever properties it |
|
| 39:39 | For whatever reason it has those I'm going to take that rock frame |
|
| 39:45 | rock skeleton and I'm going to add fluid to it or I'm going to |
|
| 39:51 | a saturated rock with a pore fluid I'm going to change the modules of |
|
| 39:55 | poor fluid in that saturated rock. gas mains equations are concerned with how |
|
| 40:02 | change in a pre existing rocket doesn't the rock from its constituent components and |
|
| 40:11 | why it has a chance of being . And I will point out get |
|
| 40:16 | gas mains equations are the low frequency of the more general B. |
|
| 40:22 | Equations which consider high frequency. So , gas mains equations are considering a |
|
| 40:31 | volumetric compression. Um so they're really for waves, therefore a static |
|
| 40:41 | Now, we're going to assume that we're near zero frequency with seismic |
|
| 40:47 | that gas means equations are applicable, keep in mind, there is nothing |
|
| 40:52 | say. They should be acquitted applicable high frequency laboratory measurements. In |
|
| 41:00 | as far as we could tell, though the more general B. |
|
| 41:04 | Theory is very important and explains a I've really never seen a very good |
|
| 41:15 | between theory and measurement. However, theory has predicted phenomena uh that we |
|
| 41:22 | observed. So maybe it won't predict precisely, but again, it will |
|
| 41:31 | things happening that that we have seen . And I'll talk about that some |
|
| 41:39 | when we get to the bot But anyway, right now we're at |
|
| 41:44 | low frequency limit of the B. . Theory. And for for the |
|
| 41:51 | to work, we have to assume few things. The rock is |
|
| 41:56 | tropic and homogeneous, if there is that needs to be handled in a |
|
| 42:01 | way and what I mean, I don't mean every microscopic point in |
|
| 42:06 | rock is the same. I'm saying the properties of the skeleton are the |
|
| 42:13 | every place and the properties of the are the same every place. That |
|
| 42:18 | means a homogeneous distribution of fluid throughout rock. Uh And that's an important |
|
| 42:28 | which we're going to come back to . We don't have to assume the |
|
| 42:35 | module us have is independent of the that falls out of the theory. |
|
| 42:43 | the theory assume, you know that theory predicts that that the shoe modules |
|
| 42:49 | not depend on the both modules of fluid. But the theory assumes that |
|
| 42:56 | there's only a mechanical interaction between the and the solid. So in that |
|
| 43:02 | , this is an assumption then that sheer modules is not affected by the |
|
| 43:08 | and number three covers that. It's affected by the fluid because the medium |
|
| 43:13 | chemically inert. Ah But really there no other, no other kind of |
|
| 43:21 | uh stoke geometrically or not between the and the solid material. Also, |
|
| 43:29 | poor fluid is firmly coupled to the . There's no capitation. So this |
|
| 43:34 | not in the near field. We're talking about a massive explosion. We're |
|
| 43:40 | about a very gentle change in the amplitude and there's no capitation, no |
|
| 43:47 | . Everything is nice, beautiful laminar . And the big one. The |
|
| 43:55 | pressure is a quick liberated between the . So, these pores are all |
|
| 44:02 | connected, meaning that as the wave through the rock, and remember, |
|
| 44:08 | a zero frequency compression, there's time these pores are connected and their sufficient |
|
| 44:16 | for the poor pressure to equip vibrate the rock at higher frequencies. You |
|
| 44:21 | to think about the permeability connecting these . The pore throats. Will there |
|
| 44:27 | given the the ability of those poor to transmit the fluid? Will there |
|
| 44:33 | time during the passage of the way the poor pressure to equip vibrate? |
|
| 44:39 | the poor pressure can equip vibrate, say that we're relaxed, right? |
|
| 44:46 | ? The pore pressure quick liberates. happy, everybody is in equilibrium. |
|
| 44:51 | we're at very high frequency and the pressure doesn't have a chance to quickly |
|
| 44:55 | . That's going to make us it makes the rock stiffer. The |
|
| 44:59 | can't escape places that are being compressed uh re establish itself in places that |
|
| 45:08 | being stretched or, or less Uh So that results in the rock |
|
| 45:14 | differ again. So the high frequencies going to be having higher module is |
|
| 45:20 | velocity than the low frequency. so we're given the bulk modules and |
|
| 45:28 | of the fluids, and if we a fluid mixture, that's an effective |
|
| 45:33 | , and at low frequency, we Woods equations are applicable, but at |
|
| 45:38 | frequency, we're not sure there they applicable. Maybe we have to use |
|
| 45:42 | else. Uh and we have the , the effect the bulk density of |
|
| 45:49 | fluid mixture in the pore space. , we're gonna we're gonna treat that |
|
| 45:54 | mixture as one phase. And that that look going to the low |
|
| 46:01 | limit allows us to do that. also have the bulk modules and density |
|
| 46:06 | the solid material. So that's the over here. And we have the |
|
| 46:12 | . Both module lists this both modules this thing and the density of this |
|
| 46:17 | , at some known fluid saturation or some known flu effective fluid modules, |
|
| 46:24 | could be that we're dealing with the fluid at different temperatures. And we're |
|
| 46:29 | the change in the rock module lists temperature. Right? So, it |
|
| 46:33 | be the same fluid, It's not changing saturation, it's just changing effective |
|
| 46:39 | in the pore space. And given these three things, we're going |
|
| 46:45 | compute the bulk module? Is that other saturation or at any other fluid |
|
| 46:52 | ? So a typical example given a sand, p wave velocity computer, |
|
| 46:57 | van, p wave velocity. And so I just ran through this |
|
| 47:04 | last time and I think we should at it a little bit more |
|
| 47:08 | So This is VP- two. So the VP equation would be the |
|
| 47:13 | root of this whole thing. And see that this is really the numerator |
|
| 47:18 | our Cape list. Four thirds mu and over density. So this is |
|
| 47:24 | the regular p wave velocity equation. K plus four thirds mu has been |
|
| 47:31 | substituted with this ugly expression And there two parts to this expression. There's |
|
| 47:40 | skeleton. So here again, we're terminology on you or notation on |
|
| 47:48 | What they mean is K dry Right. So this these are the |
|
| 47:53 | module. Light. So K plus thirds view of the skeleton mu is |
|
| 47:58 | affected by the fluids. So essentially going to compute a saturated modules by |
|
| 48:05 | this term in this term then uh you the increase in both modules of |
|
| 48:13 | rock due to the fluid. All . So this is the fluid |
|
| 48:21 | Um so what's in here, KB the dry frame. Kay asked is |
|
| 48:28 | solid material ferocity is there? And fluid module us. So what happens |
|
| 48:37 | we change these things? Well? as our dr Frey module lists approaches |
|
| 48:47 | solid module lists, This goes to . Right? So the effect of |
|
| 48:56 | fluid becomes negligible and this then just the solid module lists and we have |
|
| 49:05 | velocity of the solid material. What as porosity goes to zero As prosperity |
|
| 49:14 | to zero you lose this term. if you work through the algebra uh |
|
| 49:21 | find out that essentially this becomes the module us again. What happens as |
|
| 49:29 | rock frame becomes more and more That's the interesting thing. If I |
|
| 49:36 | ferocity the same And I make this frame go towards zero. We're gonna |
|
| 49:45 | to play with the math a little and figure out where this goes. |
|
| 49:49 | we'll come we'll come back to that a bit. So this is just |
|
| 49:57 | the equation again, gee I thought fixed this there, I fixed it |
|
| 50:02 | . Okay, I kept the bad . Um so this is the same |
|
| 50:06 | equation before. But with different Remember this? This theory assumes where |
|
| 50:18 | mechanical. So if there is no between the fluid and the solid |
|
| 50:24 | then the skeleton frame is the dry frame. And in the theory. |
|
| 50:30 | throughout the literature they refer to this the dry rock. Uh ma july |
|
| 50:37 | really bothers me. Um because there that chemical interaction in one should not |
|
| 50:44 | that if one measures the properties of dry rock, that they can just |
|
| 50:49 | those dry rock properties and do the substitution, you have to take into |
|
| 50:55 | the fact that the rock skeleton properties on the fluid it's in contact |
|
| 51:00 | So we'll come back to that idea by the way, we pull density |
|
| 51:05 | to the other side. So this roe V. P squared. You |
|
| 51:09 | realize what is roe V P That's the plane wave modules or sometimes |
|
| 51:13 | the P wave module stats I Uh but we're going to use them |
|
| 51:19 | in a bit. Um so don't this m with the M that's going |
|
| 51:25 | come And we changed the terminology of notation. We use dry, we |
|
| 51:32 | matrix here instead of solid. But think you can see that this is |
|
| 51:37 | same sort of form we saw And apparently This guy looks very |
|
| 51:44 | one -K. Dry overcame matrix. that is called the B. O |
|
| 51:50 | . And so we need to understand this bot coefficient is. By the |
|
| 51:58 | , let me make a point Everything else being equal? What happens |
|
| 52:07 | I decrease the porosity here in this ? Does this term get bigger or |
|
| 52:19 | ? So does this term get bigger smaller? Look at the equation and |
|
| 52:26 | about it. What happens as porosity smaller when they get bigger because |
|
| 52:42 | let's fluid interaction with the dryer Yeah, I mean, oddly |
|
| 52:51 | if I keep ferocity constant. I'm , as I change ferocity without changing |
|
| 53:00 | bulk modules of the, of the . The fluid effect gets actually bigger |
|
| 53:08 | . Remember the porosity here is magnified a small number here, whereas |
|
| 53:16 | its occurrence over here is divided by big number. So, relatively |
|
| 53:21 | this term is dominant there in the , S. A ferocity gets |
|
| 53:30 | This whole thing gets bigger. Isn't that weird? The smaller the |
|
| 53:42 | , the bigger the fluid effect. a little bit counterintuitive. And the |
|
| 53:48 | is counterintuitive is because we're assuming K is independent of the porosity when we |
|
| 53:55 | that. In fact, as you the porosity smaller, K dry is |
|
| 54:00 | to get bigger and that's going to in the opposite, that's going to |
|
| 54:05 | in the fluid effect getting smaller and makes sense as porosity goes to |
|
| 54:10 | We should have no fluid effect, that's only because K dry approaches case |
|
| 54:15 | . If we, if we kept dry Smalling than K solid as porosity |
|
| 54:21 | to zero. Uh, we would an enormous fluid effect. So |
|
| 54:27 | very strange. But doesn't it make for K drive to follow ferocity and |
|
| 54:34 | direct sort of Yeah, yeah, , no, that's fine. |
|
| 54:39 | I understand, you know, as said early in the class, we |
|
| 54:44 | are a very common source of error to vary a parameter in the rock |
|
| 54:50 | equations without realizing that the parameters or of them are dependent parameters. There |
|
| 54:57 | all coupled coupled to each other. changing prosperity without changing K dry leads |
|
| 55:04 | a very unusual conclusion. But it's a valid conclusion in the sense that |
|
| 55:13 | can conceive of a low porosity rock a lo que try. In |
|
| 55:20 | we saw one right here. We have a uh we've decided this |
|
| 55:28 | be a low porosity rock and yet . D must be pretty small in |
|
| 55:35 | to have this low velocity here. for the dry rock and has the |
|
| 55:42 | telling us we're having a big fluid as a result. So it's |
|
| 55:51 | You know, the the equations are and and it is possible for K |
|
| 55:58 | and ferocity to not be coupled to other. It's just that in |
|
| 56:02 | our intuition tells us that they are right. The higher the porosity, |
|
| 56:07 | more compressible. The raucous. And what our experience tells us. But |
|
| 56:13 | could be an unusual rock where that's the case, like a highly micro |
|
| 56:19 | rock. Okay, so given, , we're going to say that this |
|
| 56:32 | , the bl coefficient is one minus dry over K solid. And so |
|
| 56:37 | to Math Coz Handbook he uses K instead of case solid. And so |
|
| 56:44 | just turns this around and says K equals K zero times one minus |
|
| 56:51 | Okay, so what is beta? , it turns out that what it |
|
| 56:58 | , is the change in pore volume by the change in total volume at |
|
| 57:06 | constant pore pressure. All right. I'm going to compress the rock. |
|
| 57:11 | not gonna allow poor pressure to Which is easy to do in a |
|
| 57:16 | rock. Right? It's the air so compressible that I don't have to |
|
| 57:21 | about poor pressure. And uh so change in volume of the pore space |
|
| 57:29 | by the change in volume of the for the dry rock. Uh |
|
| 57:35 | And you can write this as porosity the bulk modules of the dry rock |
|
| 57:41 | by what is called the pore space compressibility. Right. So this K0 |
|
| 57:49 | an elastic module us in terms of pore space and this turns out to |
|
| 57:56 | equal to one minus K. Dry K zero. So, that explains |
|
| 58:02 | what beta is. I haven't gone all the theoretical connections and I think |
|
| 58:07 | beyond the the scope of the course derive these. But Bada Bada, |
|
| 58:13 | that And turns out to be All right. So, uh, |
|
| 58:19 | can write gas men's equations as Cassatt K drive plus beta squared times the |
|
| 58:28 | of that fluid term. Here's beta in the numerator. So the rest |
|
| 58:34 | that fluid term is one over Right? So am can be written |
|
| 58:47 | , does that look familiar? That's form that is looking a lot like |
|
| 58:53 | Royce average. Keep in mind that is not the plane wave modules |
|
| 58:59 | That's just an arbitrary ah now, is that is a fictitious modules but |
|
| 59:10 | acting A lot like a Royce average of 1 - Porosity here, which |
|
| 59:15 | the solid volume. It's beta minus . Okay, now, what's interesting |
|
| 59:25 | As Cady approaches zero What do gas equations approach? Right, so, |
|
| 59:34 | not going to set Katie all the to zero. I'm saying As it |
|
| 59:40 | towards zero. All right. Um What happens to beta as KD goes |
|
| 59:52 | 0? Well, beta is one KD over Ks. So as KD |
|
| 59:58 | zero, beta approaches one. So as Katie goes toward zero, |
|
| 60:07 | not zero yet. But it's approaching bay. This M is approaching the |
|
| 60:14 | average of the fluid and the Do you see that? Yeah, |
|
| 60:22 | makes sense. Oh, so if skeleton had no uh coherence coherence to |
|
| 60:36 | and it did not have about module , what would we have? We |
|
| 60:41 | have a suspension. What would the modules First suspension be the Royce average |
|
| 60:47 | Woods equation? Right. Same So gas mains equations reduces two Woods |
|
| 60:57 | As the frame module is ghost towards . That's important. We're going to |
|
| 61:03 | back to that in a bit. , so for unconsolidated sediments, that |
|
| 61:15 | small frame module is not very well ified we have a large larger beta |
|
| 61:22 | dry is smaller. So beta is for well lit defied sediments. Que |
|
| 61:28 | starts approaching K solid, so beta going to zero. Okay, so |
|
| 61:43 | doing a fluid substitution typical case will with the brine saturated velocity here and |
|
| 61:56 | add gas. And the way we gas is we calculate the effective modules |
|
| 62:03 | the gas brine mixture, K. . So in gas mains equation. |
|
| 62:10 | we're only changing KF gas mints So we start with the with the |
|
| 62:21 | saturated rock and I'll show you in minute how if we have the Dp |
|
| 62:27 | and density of the rock, we calculate K dry. So we start |
|
| 62:31 | the brine saturated rock, we know ferocity. The only thing we're changing |
|
| 62:35 | K fluid here que fluid coming from equation. And if we have a |
|
| 62:45 | gas in the compressible compression, als rock frame that gives us a big |
|
| 62:51 | in velocity here. So just a percent. Remember, Woods equation is |
|
| 62:57 | by that smaller module lists and it's an on off switch at low |
|
| 63:02 | So when we have a big drop velocity and then the velocity comes |
|
| 63:09 | Why? Because the module is has pretty much all the way, it's |
|
| 63:13 | going to change much anymore, it's to approach the gas modules, but |
|
| 63:17 | already almost there by here and now start as we add more gas, |
|
| 63:23 | dropped the density and so the velocity back up. By the way, |
|
| 63:30 | plot is here, just for historical . This was one of mike battles |
|
| 63:35 | . Right? So, so these this was his calculus calculations. So |
|
| 63:40 | the p wave velocity and there is sheer weight of philosophy. It's an |
|
| 63:45 | scale here. But you're seeing the effect on the shear wave velocity. |
|
| 63:57 | , so, uh this is a different way of doing things. And |
|
| 64:04 | of starting with the brine saturated Uh this is from Todd Smith's uh |
|
| 64:10 | paper in geophysics in 2003. He's with the gas saturated rock. And |
|
| 64:15 | saying, Okay, in my zone with gas, what would the velocity |
|
| 64:20 | densities have been had it been filled Brian? All right, So, |
|
| 64:26 | he's doing the fluid substitution at every . And where you had no |
|
| 64:31 | He's just repeating, you know, the measured locks. So red are |
|
| 64:36 | measured logs. Blue. Here is fluid substituted log where he's taking the |
|
| 64:41 | out and he's putting brian, he's creating a model. Yeah, he's |
|
| 64:51 | do a synthetic and say, my said, you know, if if |
|
| 64:56 | rock had been filled with brian, would have looked like this and then |
|
| 65:00 | to it looks like this. It two different synthetics. Okay, |
|
| 65:08 | So, you can see shear wave doesn't change very much. You had |
|
| 65:11 | . It decreases a little bit. change in density. This is a |
|
| 65:15 | rock. So it's a big change density and a big change in |
|
| 65:24 | Okay, this was a 20% porosity . Um and it was a very |
|
| 65:32 | gas being added and so couple of wham drops it all the way down |
|
| 65:41 | it was porous, 20% porosity. there's a big density effect. Noticed |
|
| 65:46 | I've really magnified the scale here emphasize the differences. So gas often |
|
| 65:52 | this precipitous drop oil's having a velocity . I'm more similar to brian. |
|
| 66:00 | a more gradual change. And so was a light oil, but it's |
|
| 66:06 | light dead oil, right? And is a heavy oil. So in |
|
| 66:11 | , we're actually increasing the velocity in case with the heavy oil. But |
|
| 66:17 | module I am more similar to So the effect is more linear and |
|
| 66:24 | from woods equation. Okay, a of different forms. This was from |
|
| 66:32 | White, famous professor at colorado School Mines and I believe Gregory and his |
|
| 66:40 | uses this form as well. There some more convenient forms, I really |
|
| 66:47 | this one to conceptually think about Gaston's because it's very symmetrical. So uh |
|
| 66:56 | uh this form originally came from brown Karenga, you could find it in |
|
| 67:01 | coz papers and in his hand it's a little bit inconvenient to use |
|
| 67:06 | you haven't explicitly solved for anyone but it's it's very nice and symmetrical |
|
| 67:15 | easy to remember. So, uh you look at the ratio of the |
|
| 67:21 | modules to the difference between the solid K. Zero and saturated, it's |
|
| 67:27 | to that same ratio for the dry and the ratio for the fluid uh |
|
| 67:35 | the additional multiplication by the porosity So again, looking at this |
|
| 67:44 | if we're thinking about how much this changes, you could see that everything |
|
| 67:51 | being equal. The lower the Yeah, the more that's going to |
|
| 67:59 | because this term is being magnified, lower the porosity is, the more |
|
| 68:05 | the fluid module lists changes the saturated from the dry modules. Okay. |
|
| 68:17 | , we're often faced with the situation we have measured V. P. |
|
| 68:24 | . S and density and we want determine what the dry dry frame modules |
|
| 68:31 | . So that we could then change fluid module. So that requires that |
|
| 68:35 | know the composition because I need to The solid grain module is K0. |
|
| 68:42 | need to know the pore fluids and temperature pressure conditions and validity of the |
|
| 68:48 | and gas oil ratio, gas all these things. Uh And use |
|
| 68:54 | bats of long equations. However, get the fluid module lists and I |
|
| 68:59 | to know the porosity and if the it is a low, you need |
|
| 69:03 | know it very accurately. Um And I can then do is I could |
|
| 69:09 | out the dry frame modules. um could also do the math and uh |
|
| 69:19 | here, you have gas mains equations written before, for the saturated modules |
|
| 69:27 | kes is the saturated module us. , so um anyway, from V |
|
| 69:38 | and density, you can get all these things because roe V P squared |
|
| 69:42 | capable is four thirds mu uh B square, roe V S squared is |
|
| 69:48 | So I could get cassette and mu these other things I have to |
|
| 69:53 | and then I could get the dry and then I could change the fluid |
|
| 69:58 | is and see how the, see the saturated modules is going to |
|
| 70:05 | Yeah, Okay, so I have notes here, in case you ever |
|
| 70:10 | to uh program this up and matt or someplace. Um and so I |
|
| 70:17 | take you through it. Uh they're there, I won't bother going through |
|
| 70:23 | again. Uh And just for historical again, here was the first sub |
|
| 70:29 | I ever wrote to do fluid This was for trans. So it |
|
| 70:34 | you how ancient I am, And actually uh four lines of code. |
|
| 70:41 | much so. Pretty simple thing to to do. Woods and Gardeners |
|
| 70:52 | Say that again? I was asking it did a gardener's equation as |
|
| 70:57 | Oh, this little equation, I know. I haven't looked at the |
|
| 71:00 | in ages. Uh curious. Let see, Yeah, I guess it |
|
| 71:09 | because you it computes fluid density, , no, this is going |
|
| 71:16 | What's the input water saturation? So must go through Woods equations. It |
|
| 71:25 | ves Oh, and yeah, so uses, you know, the Greenberg |
|
| 71:33 | equations, fluid modules there. It , it uses Woods equation. |
|
| 71:40 | so anyway, simple little guy. , so this these equations are valid |
|
| 71:52 | you have a homo genius distribution of over a wavelength, say, and |
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| 72:02 | you're at low frequency. But what if you don't have a homogeneous |
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| 72:11 | And this is where the patchy saturation , This also came out of math |
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| 72:15 | guys at stanford. And it was very, very clever realization. The |
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| 72:23 | saturation model is this where my Uh and assuming it's got consistent properties |
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| 72:33 | place. So, I have a rock, and I have parts of |
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| 72:36 | rock colored blue here, which are in water. I also have patches |
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| 72:42 | arbitrary shape and size saturated with oil , and other patches that could be |
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| 72:49 | with gas, or maybe it's only and water and oil, only gas |
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| 72:53 | water. But the beautiful, beautiful that um africa realized was that if |
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| 73:01 | is the same rock, every then the sheer module list must be |
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| 73:06 | same every place. And when you inclusions with the same sheer module |
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| 73:13 | A wonderful thing happens if I have of arbitrary shape, but the sheer |
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| 73:26 | is is the same every place, have a Royce average of the |
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| 73:36 | So, the module lists the plane module lists for the composite depends on |
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| 73:44 | plane wave module I of the Right, So the saturation is represented |
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| 73:50 | the volume of each patch. So the volume of red is the |
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| 73:56 | saturation. The volume of oil is water saturation volume of uh water is |
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| 74:03 | water saturation. So the saturation of saturation of oil, saturation of |
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| 74:09 | And the sheer modules is the every place, lovely. And in |
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| 74:16 | of these patches you have your uh substituted module lists for the patch. |
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| 74:25 | maybe you started with cassette for you then compute Cosac for oil and |
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| 74:32 | for gas. And so the effective of this composite if these are all |
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| 74:38 | relative to a wavelength is given by beautiful. It's just just a Royce |
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| 74:52 | . And if you cross plot Apache versus a uniform distribution and this is |
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| 75:01 | case of just changing gas saturation. , I have 100% water here, |
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| 75:06 | gas here. And to make a convenient plotting impedance. So this is |
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| 75:13 | times velocity for the patchy distribution, far more linear than for a homogeneous |
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| 75:24 | . I have a homogeneous distribution, have that on off switch from woods |
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| 75:29 | , but for a patchy distribution more . Okay, let's go back to |
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| 75:45 | simpler case. Uh, you there there is, you know, |
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| 75:50 | I said, this is a very idea, very interesting. You have |
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| 75:54 | ask yourself why you would have different if the rock is the same every |
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| 76:01 | , right? So if the sheer really were the same, why would |
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| 76:05 | have these different patches? On the hand, you could say, |
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| 76:08 | maybe there are slight changes in sheer is associated with big changes in poor |
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| 76:14 | or permeability, whatever, resulting in patches. And you could ask yourself |
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| 76:22 | C2, is this likely to be stable situation? I mean, give |
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| 76:29 | a little bit of time. And these guys going to try to stratify |
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| 76:33 | density? Right. Would you actually something like this? Especially in a |
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| 76:41 | reservoir? I think geologically within 100 , this kind of situation might |
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| 76:48 | but over the uh timeframe of production a reservoir, it is conceivable that |
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| 76:56 | may wind up with patchy distributions like . Uh one more reason why time |
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| 77:02 | monitoring gets really complicated. Okay, , uh just to summarize the kind |
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| 77:11 | things that we think we know how do now, uh here we're taking |
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| 77:18 | constant rock frame. We're not letting rock framed properties change with death, |
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| 77:24 | we're taking that rock and we're putting at different depths. Right? So |
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| 77:29 | porosity hasn't changed with that. The thing that's changing are the fluid |
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| 77:37 | And we're seeing that that particular if it's filled with gas is going |
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| 77:43 | be have a strong depth dependence, the brine, saturated rock and |
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| 77:52 | Oh, I'm sorry. Okay. , the porosity is the same, |
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| 77:57 | the rock frame module is is changing death, Right? So ignoring the |
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| 78:04 | in porosity, but just taking the of the effect of pressure on the |
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| 78:11 | front. Okay, so two things happening, pressure affecting the rock frame |
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| 78:17 | pressure and temperature affecting the flutes. again, you can see that heavy |
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| 78:23 | and water are pretty similar. here we have a dead light |
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| 78:29 | Um, and here we have a life oil. The light live oil |
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| 78:34 | closer to gas, but of course having the lowest velocities. And I |
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| 78:41 | realized I'm at a time. So questions, I will stop |
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