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GEOL7325 Petrophysics and Formation Evaluation - Day6 10-14-23 AM
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00:00 Today, we're gonna wrap up So we've gone through progressively, gone
00:08 Archie's Equation. We've figured out how get the parameters for it started with
00:15 . And it goes down to Last time we looked at resistivity
00:20 we got uh our A Yeah. . All right. So today is
00:39 last one is Archie's M and N we're gonna look at. So geologists
00:44 theory should like this because it involves at rocks to determine what these are
00:51 out. The importance of that turns , although there still seems to be
00:56 a bit of discussion over this that fairly simple, at least to get
01:00 first to order, look at what parameters are. And I hope
01:05 uh after this, we have a exercise. I don't know how short
01:09 is, but we have an exercise we can go through where we're gonna
01:13 some of these for uh carbonates. then I really would hope we can
01:19 to uh looking at Shay Sands today would uh wrap up the course except
01:25 gonna have a lab tour. And next Friday, if uh Professor Haen
01:32 still willing to help. She has , she, she has a unconventional
01:38 that she can give, which is for a lot more reasons to wrap
01:42 the course. Because with these unconventional looked, you've gone through the looking
01:47 , the rules are off. So a nice contrast to what we do
01:51 convention. Things really are different. she's gonna talk about how to get
01:57 there. There's actually been quite a of supplies, but we'll see how
02:02 we get around lunch. We'll decide to come back here or go directly
02:07 to do the lab tour. Uh on how interested you are, how
02:11 questions there are that can take 22 . So we might be able to
02:17 here for a little bit after lunch work on she sands. So I
02:28 to start out by confusing people. what I'm gonna call this is a
02:32 effective medium model for electro electrical And all that means is that we
02:38 going to look at the various we're gonna put together a rock.
02:43 find it quite visual, right? intuitive, but uh that's not always
02:49 by the people listening to the So I would encourage you to ask
02:54 . So I really think this gives a lot of insight into a resistivity
02:59 as well as permeability tells you what role of puck force structure is
03:04 on those measurements. Which kind of to our understanding of the rocks and
03:10 can get a lot worse, believe or not. What we're gonna do
03:14 , all we're gonna worry about is conductive inclusions. OK? If you
03:19 conductive inclusions, things get uh more . Just recently had a master's student
03:26 on that and Grace did a good . So what are our goals?
03:31 goals are to develop an intuition? does an M star or M of
03:37 mean? What does it mean if two? What does it mean if
03:40 2.3 in a, in a in a carbonate? Similarly, you
03:46 get as low as 1.6 all the up to almost three. So what
03:51 that mean to have that quite a range of values? And how does
03:55 relate to the core structure? Then gonna tie that into permeability. We
04:01 resistivity. We go a long ways understanding the permeability, particular tortuosity.
04:10 those are our goals. Some of is gonna be repetition, but I
04:13 to refresh your memory. It's been while since we talked about some of
04:18 . Uh this was our nomenclature. What is our w it's the resistivity
04:23 the water? Why is it so ? Because basically the entire resistivity scales
04:29 this number. If I double the resistivity, I double the resistivity of
04:35 rock. So it, it is the heart of what the resistivity is
04:40 . All we have to do in conventional rock with this like this with
04:46 is we have to figure out the of the rock on our w this
04:51 gonna be different from when we study Smith's equation where this simple scaling is
04:58 gonna work. So it's not gonna linear with the resistivity of the
05:03 And what that tells you. Oh That was an apparent the A
05:18 for a parent. And that was we left oil saturation calculations out of
05:23 calculation. So we calculated, we we set RT equal to RO if
05:30 remember that. So no saturation We calculated everything as if there was
05:35 oil. And so all we were was taking out the porosity dependence and
05:42 and then you look for the lowest of RW A and those will be
05:48 to RW. That'll be our estimate our W. So if you looked
05:53 the Swiss come out of the exercise , so what you would be looking
05:59 there was essentially nine samples that were water, 100% water saturated. There's
06:05 three that had oil. So you to exclude those three and then you
06:10 take the RW calculate from the other average, then you get your best
06:16 of RW. That is the best . A. Calculations are the best
06:21 to get RW as long as you're that they're 100% water saturated. You
06:27 a wet zone to do that. you get, you can also get
06:33 from the pickup plot that you noticed . But the problem with that is
06:37 extrapolating data along ways, right? that's not, there's significant error inherent
06:44 doing that. So should be getting from the picket plot RWRW from an
06:51 A calculation and then matrix parameters from Hingle plot kind of the strengths of
07:01 three techniques she did yesterday. And the whole goal, I don't know
07:05 you are in the exercise will be close. But a lot of times
07:09 will actually iterate through those three calculations get your best numbers that best fit
07:15 of the data. So it's, a nice if, if you don't
07:19 coord data, if you don't have else. But the log this is
07:22 reasonable way to approach an evaluation which the point of it core is still
07:31 . All right, remember I got good question and then RR zero,
07:36 ? Just means zero. Just we're setting RT equal to ror
07:43 And that just means we're leaving the calculation out. This is the resistivity
07:48 the water saturated rock where the water is 100%. Yeah. NRO is
07:58 greater than our W so I really this mental model to me to do
08:03 visual makes an enormous amount of Not only for memory, but
08:09 as long as this kind of model up and remember we looked at these
08:13 we started with this cup full of . We measured its resistivity,
08:19 Or just the water that gave us w obviously. So we just have
08:24 uniform electric field across this parallel field , et cetera. So that measurement
08:32 , the resistivity again is an intensive . It's a it's a property of
08:38 water that the size of that Yeah. Then we added rock to
08:43 . Literally, you just dump sand this. Conceptually, what's gonna happen
08:49 my resistivity will get bigger even though , the rock is nonconducted. This
08:55 where things are gonna change when we clays because then we have another conductive
09:02 . So Archie's equation does not you have to extend it.
09:07 Or find out how wax and smiths me is still the most reasonable method
09:12 do that. So that's the next we where we add rock plus
09:19 And the last thing we're gonna do add oil once we think about adding
09:24 to this. So in general, form that this takes RO is equal
09:30 a formation factor two times RW. I mentioned, this is important because
09:36 scales linearly with RW. So if double this have this, it's reflected
09:44 in the resistivity of the rock that us that this formation factory is a
09:50 it's not changing, it's independent of . Again, it will not be
09:56 for Shay Saint. OK. And the magical part to me is this
10:02 equals one over B to DM. you notice what we did yesterday,
10:07 extrapolated this, our data all the to a pro of one that allowed
10:12 to determine RW when the ferocity is . Our tub is full of only
10:21 . We also extrapolated this equation all way to a ferocity of zero.
10:27 did that through a Hingle plot. that allowed us to get a matrix
10:32 right back to our matrix, our travel time or our matrix density,
10:40 example, which is what you use calculate porosity should have got right around
10:47 , which indicated it was elastic. the matrix density of quartz. Some
10:57 you got more like 2.672 0.63 or , which it certainly can vary.
11:03 you have a little bit of belt , that'll be a little less than
11:07 . If you have high rate or like that, it can be higher
11:10 265 again. So that number is diagnostic to your mineral, right?
11:16 we had, if we had obtained what would that mean? Limestone?
11:24 . 2.8 dolemite. They're all questions might encounter on your final. By
11:32 way, there's some variation of This brings us to this expression,
11:38 is often used by people. And only use this because they really haven't
11:43 at their rocks. They don't understand going on. Uh for a plastic
11:48 sea will typically be quite close to in a carbonate. However, that
11:54 can be very different from the It's because of the more complex core
12:00 you have. So one way to at the lecture today is we're gonna
12:04 how to get the value of C . What that means? Right?
12:10 cements put an X through that, is a misnomer. Cements do not
12:16 much to do with revisit. I never 30 years of looking at these
12:21 of data seen. One instance where had a major impact on the
12:28 Velocity is absolutely not true. Velocity be very sensitive just a few percent
12:36 , particularly uh if you worry about it's distributed. If it's distributed at
12:41 grain context, just one or 2% can make a very big difference in
12:47 velocity in your modules of your right? At brain modular, we
12:52 at uh related, related to the calculation, right? And so our
13:00 is to basically find M MC. gonna do that by looking at 10
13:06 which geologists should like geophysicist gets there him useful for you too. So
13:14 , it's a Power Law, we in detail about why it was a
13:17 Law. Here's the RW A, left the saturation out. The last
13:22 we're gonna do is add oil to . This model conceptually works extremely
13:28 We are gonna follow these steps. we figuratively build a rock, a
13:35 model for a rock, we are add the sand. We are gonna
13:39 oil aggressively to figure out how that the resistivity. We're gonna fly.
13:47 We're gonna fly what that means as impacts on the to velocity for
13:52 we are gonna have to add, gonna have to add this rock in
13:56 different ways. We're gonna have to matrix porosity and we're gonna have to
14:00 bugs because they will affect permeability and very differently. And for the
14:07 we're gonna add the grains, we're first add the quartz and then we
14:13 add clays. OK? And those affect the reason, even even if
14:19 at high salinity where the connectivity of clays doesn't matter. It still affects
14:24 core structure. We'll see exactly So this impressed me when I first
14:33 , took a long time ago when first uh entered the oil industry,
14:37 working on uh my thesis which was optics, basically shooting down missiles,
14:45 ? Or turning red light into But uh the cemetery here, I
14:50 know if geologists, geologists would like symmetry too, right? So the
14:55 between what it our mathematical model looked for the formation factor was our law
15:03 an exponent OK. Scale with this this formation factor if you look at
15:11 is this one be exactly the same is going OK. They are scaling
15:17 resistivity of the water saturated rock. a parameter here, right? This
15:23 of it uh remains relative remains constant an individual rock as we change our
15:30 , right? That resistivity index changes what like what happens when the porosity
15:36 , it both obey Power Law. this is a clue as to how
15:41 resistivity is gonna work. Now, gonna add, this will be a
15:46 case of a LIH change. If think of adding oil or actually
15:52 or we're lowering our water saturation or oil in the pores. So why
15:58 other lithograph changes behave in the same the intuitive argument to it? We'll
16:04 how that works in a minute. with me so far. What we're
16:09 , Archie's equations play with Mark Uh There's nothing special about N equals
16:16 other than it's a single button on calculator. So that's the only reason
16:20 think it's popular. Uh It's a harder to take logs and do the
16:26 power rate rather than two. But we will see and not too long
16:33 M or an N of two means we have a fairly shay sand that's
16:38 quite a bit of clays in the . So we shouldn't be guessing
16:42 unless you know, you have significant of clay, maybe half your course
16:49 is included with. And see we're figure out what it, this various
16:58 . I don't know if any of have been looking at Duan.
17:00 it, it is a good I still recommend the book. I
17:04 that a couple of you have them on the desk. I still have
17:07 digital copy if you like it. The only complaint I have about
17:11 it's starting to get a bit dated in terms of some of the logs
17:16 and they have the newest logs in . Uh But for the logs,
17:19 course it's just fine, the logs covered. Um The other thing I
17:24 like is that he was now, he was SLV and uh J back
17:34 and he has a very biased but he has a biased, uh
17:38 of uh idea about uh core and value of the core people disagree.
17:44 hope it's a little sensitive to right. Uh My personal opinion,
17:49 you absolutely do a rigorous evaluation of formation. You need a core.
17:54 least need some look at the right? So I, I don't
18:00 , uh I don't think I uh to have an uncle who was a
18:05 , but I, I doubt a would really be working on trying to
18:10 a sample unless they knew it was or brass or steel or tungsten,
18:17 . That's where you would start. where we should be starting.
18:21 Looking at the rocks, understanding what's , understanding what the lithograph is.
18:27 is the ferocity changing? And I'm very tempted to ask you what's the
18:32 question? A petro physicist, our should be asking the geologist and that
18:40 why is the ferocity changing? Don't that do not know how to evaluate
18:46 reservoir, the properties change in a different way. If you're changing,
18:52 or you're adding clays or your secondary or whatever that mechanism is, will
18:59 your firm, your resistivity. All these things compressibility, everything in a
19:05 different fashion and in a carbonate, absolutely essential and it's poor structure
19:14 So this is an example I give this uh this appeared in a chart
19:19 when I first got here might even current chart. I think they've taken
19:24 out. But they had a very model here for what influenced the
19:30 What was their model? The only changing mechanism they have on this chart
19:42 cements. So like I said, have never seen where we looked at
19:48 . We made resistivity measurements where cements the dominant factor. You really can't
19:56 . Yeah. So what they stated that and the range is actually a
20:01 too far, right? You really see things 1.31 0.4 at all.
20:07 alone. Uh So they will start a very regular vero and you can
20:12 this in carbonates. Uh they can as low as about 1.6 and
20:18 uh they will go up from upper end is approximately, right.
20:22 you get to a rock that's complete the poor space is completely effed with
20:28 , you can get as high as 2.3. Ok. So it's about
20:34 , it's not about, it's not cements. And this this line,
20:41 ? They, they take you haven't data, the origin of that
20:45 If somebody just regressed the data, try to understand what it this is
20:51 we looked at. So if we to build tuition, uh this is
20:56 I started, I've seen this in literature since when Peterson's book, Advanced
21:02 Physics has these kind of models in and elsewhere. But let's try to
21:07 a little bit of intuition. So take a core, we drill a
21:10 solid rock, we drill a hole it to mimic the core space.
21:15 is called a tube of a model it. People build these two models
21:19 variability too if you calculate the resistivity this. So we have RW in
21:25 four, we have 00 connectivity in rock, we put these in parallel
21:31 each other, which they are. you find is. Indeed Archie's equation
21:36 down here. And the M value one, so F is equal to
21:42 over. OK. We have How about if we take this rock
21:49 we drill two holes, same size , we drill the holes, we
21:54 the resistivity. They are in parallel each other. Uh You can all
21:58 through this yourself. You still get and you still get an Emma of
22:04 . We haven't learned a whole lot if we change the size of the
22:11 , which we've done here, we two different sized holes uh that we
22:16 the connectivity resistivity. Archie's equation still with an M of one. This
22:23 have been expected. Remember I made big deal out of this our first
22:28 together where we looked at the impact grain size on permeability. The overall
22:36 of this, the mean grain size not change the resistivity. It will
22:42 the permeability but it does not change resistivity. So the size of these
22:48 doesn't matter. OK. That's the of that. So we have to
22:54 to get something that varies from an of one. We have to put
22:59 , we have to make our tortuosity from one the tortuosity. If you
23:05 what it was when we talked about , it's the ratio of the physical
23:09 of the sample to the length of current path here. The current path
23:15 are the same as the length of sample. Yeah, so we get
23:21 M of one here. If we this hole at an angle, what
23:27 is that geez the connectivity is not by the, by the amount of
23:34 tube that is not sprayed along the field. And therefore, our formation
23:41 actually has this tortuosity. It's the of the tube which is longer than
23:47 length of the sample. It goes P squared over two. Sometimes you
23:52 see this written as the F is to P over P. And this
23:56 because they're modeling things as a diffusion process that introduces a square root.
24:02 for now, we're not gonna worry that, right? Productivity is not
24:08 , we all OK. With What that means this is really gonna
24:13 what gives us insight into the resistivity general. You can do this
24:20 If I tell if I allow my lines to be parallel to the poor
24:25 the poor space I can go through calculation and we can find that F
24:30 equal to T squared over B The nice thing about this,
24:35 This gives me basically is this Archie's right here. We can set Archie's
24:42 one over P to the M equal this two model which is P squared
24:47 P I have some intuition as what tortuosity is. You don't have
24:52 Now now is the time to speak , try to talk about it again
24:58 you're gonna get quite confused later on we understand what that is. Thank
25:05 . So what is tortuosity? we have a, the length of
25:10 back foot, put the set of it, we measure the length,
25:15 . Let say it's two inches. we measure the resistivity, weer what
25:22 formation factor is and we find that current has to go around all of
25:27 grains or I'm gonna show you a section in a bit that'll help the
25:33 paths have to go around all of grains. So the the electrical path
25:38 , the electrons have to follow, electric field has to follow. It's
25:43 longer than that length of the core my, it gets the current from
25:51 end to the other or the fluid through the pores. And so it
25:57 to all the brains, my torch than one. Yeah. Can't be
26:05 than one that's there and, or . All right. Is that
26:14 Is that OK? So that, like you will have, you will
26:19 people whether to say this or but people talk about geophysicists, for
26:26 , they'll talk about an acoustic I don't know what that means because
26:31 are averaging over the floor space and grain if I had time. And
26:37 course, we could talk about how we model it differently, et
26:42 . Give me another two weeks and can go through that. Sure.
26:47 had enough now. So the the is governed by the torture but not
27:01 size of the port. Yeah. this is why you can have
27:09 Uh chalks or whatever. And the is for per, between permeability,
27:15 repeat this difference between permeability and resistivity the electrons don't care about the poor
27:21 , right? They're just making their way, they're going through the poor
27:25 , the fluid. However, because these attractive forces is stationary at the
27:30 walls, so we have to shear . So this is why poor size
27:38 or body size, right matters with smaller, the poor, the more
27:44 we are shearing and therefore the lower permeability. And it's why viscosity shows
27:51 in Darcy's equation. You see viscosity Archie's equation. No. And that's
27:58 reason because electrons are basically unaffected by boundary condition. Yeah, that's something
28:08 can usually solve at any rate through model, right. Models are useful
28:14 not always exactly correct through this We have an expression for the formation
28:20 it's T squared over P which we went through and developed a little bit
28:24 intuition for at least the concept of . And we can actually solve for
28:32 in this equation right uh under various in terms of the coos because this
28:39 should have a feel for try we can talk about it again if
28:45 still not clear. But for M zero, if we go up here
28:50 solve this equation for M, we that the tortuosity for M equals
28:56 it's one over B uh one over to the zero, which is
29:01 right, right. So he squared to here, right. So uh
29:07 tortuosity is simply the square root of porosity just plugged into here. So
29:15 equals one P squared over B. we, we just get, take
29:20 square root of both sides, Or M equals one, the
29:25 this is the relationship we're using when solve for it. So for M
29:30 one, it's one over B, one line is 11 over P to
29:34 zero. So we get to tortuosity identically one. This is important.
29:42 this one is actually somewhat interesting, ? What happens here is that as
29:48 ferocity increases for an M of as the porosity increases the tortuosity
29:55 That's pretty odd, right? We making the four space bigger in
30:01 You would at least my intuition is the total smart as the variety of
30:11 one is actually interesting because we're gonna into four structures that do this.
30:17 ? You, you actually something like , we'll, we'll talk about when
30:20 might occur, but it's not very . We get where M equals
30:25 our usual. And what, what, what M equals one means
30:30 I change the porosity and my tortuosity remained identical. That's also kind of
30:36 , right? Really would expect my to go down. And so that's
30:40 happens if M is greater than So for M equals two, my
30:46 is actually increasing as my ferocity Right? You know, yeah,
30:53 happens then what I would ask you take away from this intuition is that
30:58 M value is telling you how quickly tortuosity changes with changing ferocity. Different
31:08 have different rates of change of tortuosity I change the amount of that forces
31:16 one of the reasons I say you to know why your ferocity is
31:22 that clays and plastic will increase tortuosity rapidly. You know, most of
31:28 are geologists. If you look at four system in L A, it's
31:32 complicated, right? So it would expected that if I'm current is moving
31:38 that four system and I add more more of that core system, my
31:43 would be getting bigger starting as a change on tortuosity but not nearly as
31:51 as places. Yeah, similar things happen with permeability. Permeability is even
31:59 because of the bound water ideas that talk about. Again, this was
32:03 important idea. Everybody's OK with this is telling you the rate of change
32:11 virtuosity with ferocity. And again, idea you didn't get a chance.
32:22 in my petro physics classes, they through and calculate uh these, these
32:27 values right? Ferocity as a function sphere paths, right? And what
32:32 happens no matter what the sphere pack hexagonal or thromb cubic. This is
32:38 example of a cubic which is one the easiest to calculate. You always
32:44 for any of the sphere packs the of the spheres. This deed cancels
32:53 . Yeah, if you didn't believe before, this is evidence,
32:57 that gee at least for these regular , right, the size of the
33:04 does not matter in calculating the And it's the geometry of the path
33:12 , permeability will change, go through . So our job is now to
33:19 at rocks. This is fun right? What happens? Uh we
33:24 , we are going to this is I've heard this from Petro physicists in
33:32 , we can model right? Carbonates basically being a superposition of three pore
33:39 , an inter granular inter particle a buggy porosity of micro porosity.
33:45 it's it's validated just by people looking thin sections, it's validated by people
33:52 NMR measurements looking at again, just to believe me because we haven't talked
33:58 the NMR. We get a chance we can can spend an hour or
34:03 . Um I can ask you what more interested in, right? And
34:07 the point is that we are looking some sort of model where we can
34:12 a pore system with an Exxon akin an Arching Exon that's valid for that
34:20 system does not change depending on how of that poor system we have.
34:27 . So, I don't know how this group is but, uh Shell
34:31 one point had what was known as Shell rock catalog. It's absolutely available
34:37 all of you. Uh, it's that much money anymore. I would
34:41 suggest that you buy a copy of for your company. It costs roughly
34:46 million dollars per sample to populate it shell. And you're getting it for
34:53 much less than pennies on the What was spent on this to actually
34:58 the data uh validate everything and organize . So it, it's a great
35:05 . And if even if you have core that you can think of in
35:08 analog, you can typically look it and that's rock catalog. You get
35:12 number of the rock properties out of . It's quite useful and not very
35:17 money. I don't know why she to sell it, but they did
35:20 one point, they didn't get that money for it either, right?
35:26 so the the rocks are described, ? Actually, only visually the,
35:32 you can see is the intra granular velocity. So even though Professor Ha
35:37 like the point counts that much in rock catalog, I did find a
35:42 of, but I, I'll leave there. Uh But uh it was
35:50 to me, at least as a petro physicist to go into this,
35:54 ? And look at the impact of forces. Ok. So let's
36:00 this is where we should turn the on. Turn all the lights
36:06 Yeah, turn them all out. gotta be dark here. So what
36:12 is is a picture. I don't if we can still see it,
36:15 the geologist. So you know what's on here, right? So you
36:19 , this is so this dark blue looks a lot better on my
36:25 It's actually the poor space. The are actually uh saturated with a glue
36:32 . So this is another soap box commonly get on these things are relatively
36:37 to produce. If you have the and you're making measurements, you should
36:42 thin sections on every sample, particularly you do an unconventional stress work on
36:48 . Right? The measuring of porosity permeability related to that spend 50 bucks
36:54 a thin section made. And if else, you can put pictures in
36:59 rough hurts and make people think you what you're doing, right? I've
37:03 at the rocks. This is uh . This is why the, so
37:08 uh I got huge pushback during downturn I used to make these on basically
37:17 own nickel because geologist still don't understand every time we did this later on
37:29 the they will, this is one the data sets that I found always
37:35 used. It's uh that that really worth it. You know. What
37:42 of rock do you have? What fourth base looks like? I can
37:45 clays in these things. I can mineralogy here. I can stain them
37:50 fell far et cetera. Professor had to worry about him. He's the
37:56 who does this for a living and enjoys silent, I guess.
38:03 the, the main thing I want to take away from this is that
38:07 described here, we have the the pre inter granular vero dominates this
38:17 . OK. So this is this is a poor type. It's
38:20 dolomite Reprisal obviously. Uh And so stone. And so we will be
38:27 this as having only inter granular right? There's a small amount of
38:33 here. OK? But it's small that I can largely ignore it,
38:37 ? The first order. So what sense to me at the time would
38:43 to plot these up? Let's go through the la rock catalog. Let's
38:48 all the rocks that have less than of the total frogs, these bugs
38:52 let's plot them and see they have single port system present. So let's
38:57 take a look at that. When look at this data, this is
39:00 global catalog, by the way, was from reservoirs all over the world
39:05 shell was involved with. What do see in this data? Fairly big
39:13 ferocity that the two, give or . Uh I calculated it happen and
39:33 know it's a lot of square over how about the to organize recording?
39:57 is no, we have values and same value at 26. That's kind
40:09 fun. Let's plot it up. you can see this, but there's
40:14 single trend that should be familiar to with the exercise you did before.
40:20 is the formation factor. So what made this is called a formation factor
40:25 , which differs from a picket How does it differ from a picket
40:34 ? How do we get from ro the organic? All I have to
40:41 is divide by our top. The RO is equal to F times
40:47 If I take the RO I divide RW, I get F. So
40:51 that means is that see, this should extrapolate to an F of one
40:59 of one. Yeah, this is problem with that C and A
41:14 She said that when I'm back to , what happens to this? The
41:24 means I gotta get a job for previous. Does it? No,
41:34 the porosity is one F is equal C That's wrong. It's wrong.
41:40 other argument, it's wrong. It to equal one formation factor has to
41:47 one virtuosity is one, meaning that length right from one end of the
41:53 to the other is the same as half length or my current. So
41:59 use this equation by what it means that this is where some people get
42:05 in a mathematical sense, locally but globally good. All that as
42:17 ferocity approaches one, I have to have to. So this will break
42:27 . If we get far enough away where we have calibrated, then we'll
42:32 what that means. Oh, uh investigate with that for a
42:43 There's my picture here are my exponents plotted up. And the good news
42:49 this is a, this is a , a dolemite back. Archie's equation
42:55 quite well with an M value of and extrapolates back. So in this
43:03 Archie's equation will work, I could a picket plot, I could get
43:09 I could do all of those different . This is one where that extrapolation
43:15 . That picket plot typically people will it in a plastic, right?
43:21 this extrapolation to an F of one of one pretty much works. We'll
43:29 when it won't even in a And then here's the plot of
43:35 So what what this means is that single exponent is valid for this?
43:39 tortuosity is changing, right? I it and being my tortuosity goes to
43:46 to 1, are they OK? this pretty standard ay kind of
43:57 Now another one, if you look the four description and they're driving as
44:05 all but and black what this means that we have a large for embedded
44:11 a very fine frame matrix where it's you cannot even see, you have
44:17 go to an that for you can these rocks. So you know,
44:25 bugs are connected to the current But these samples my property percentage
44:44 what's happening to the like I some my highest tortuosities back here over
44:55 no real trend in tortuosity, Or my M value is showing quite
45:01 nice to what the data, what went the wrong way. But this
45:20 can see there the night trend in that the of that is actually close
45:26 one is interesting and see my extrapolated is nowhere close to an F of
45:34 of one, a lot of people going on here and I was,
45:43 you can see what happens to the as a function of ferocity. It's
45:48 much independent. It's like the numbers , right? So what what is
45:54 here? We are adding bugs to matrix porosity and those bugs are not
46:01 changing the tortuosity gonna show you visually of uh what this looks like in
46:09 second, right? Remember what an one meant? Remember what an exponent
46:16 one meant? Should I go back that time gonna go back anyways?
46:25 was an MA one? My tortuosity unchanging with velocity? So all this
46:35 is that when I, when I buggy porosity. I am not significantly
46:41 the tortuosity. My tortuosity is all up in the matrix fours,
46:46 That these bugs are embedded in What, what will ultimately happen if
46:55 remember the Lucia classification that Professor Ha about, we talked about touching versus
47:02 touching bugs. The only distinction I in touching versus non touching is when
47:08 are touching to the extent that you trace your way through those buggy pores
47:13 one end of the sample to the . And then it's acting a lot
47:17 like a fracture, right? But two, all the way we defined
47:22 bug was that that core was significantly than a mean grain size. I
47:29 care if it's twice as big or , or three times as big.
47:33 don't care if it's four times as , five times as big. It's
47:36 a buck. It still behaves like bug only when they percolate. Does
47:45 matter. So what we want to this one, I might expect a
47:50 questions about, we could leave the on. I know it's dangerous to
47:54 the lights off for you. Uh I haven't had anybody injured yet.
48:00 that the equation is locally true in mathematical sense but not globally true.
48:08 that means is that a G's the derivative of AIE equation is correct
48:14 not the integrated form where we have uh over a finite region. Uh
48:21 , it's got to break down. what that means is that the derivative
48:28 correct? OK. Which is this a standard ticket derivative of a of
48:34 Power Law, right. And then plug in the value of F again
48:38 to change an F with respect to again. Well, one of the
48:41 I ask you to understand that is some slope finds the ratio of the
48:47 package of velocity. And that if integrate this right, we can integrate
48:53 over multiple steps. So adding each system independently, in fact, adding
49:02 , right, adding oil to the is one of these stuff. This
49:07 if you're not familiar with, it means product. You're probably familiar with
49:11 sigma and the sum. But uh product is just uh this just
49:16 pick the product of these multiple Well, it's so it's,
49:26 it's called lambda because it's only gonna locally true. M is a slope
49:32 whatever my final formation factor and gravity to an f of one P of
49:38 . The slope of that line is , the slope of a local tangent
49:43 the curve is lambda. I, , I'll show you that in a
49:48 and we're gonna go through an exercise you can do this yourself. But
49:52 is a little bit confusing. All . And then if my last porosity
49:57 due to oil then, and we that in then my last core system
50:03 , right, my porosity change is to adding oil. My exponent then
50:08 equal to N for that. And and behold, we recover Archie's equation
50:13 the saturation dependence. But this is because people say gee this can't be
50:20 . Well, you people have been this since the original inception of RG
50:26 . The only idea here is to it to allow multiple four systems.
50:38 this one you can actually probably So what what's going on here,
50:43 is the idea when current is So we have a matrix ferocity,
50:47 have significant matrix ferocity. We have buggy ferocity which is like do like
50:54 stone. But what, so you're your fluid or your current is having
50:57 go around all of these grains significant associated with this and then we hit
51:03 bug and the current or the fluid zip straight across. So is this
51:09 the tortuosity? No, but this system obviously, if I change the
51:16 of this board system, right, a sorting or whatever related that my
51:21 will change. Yeah. So we get what happens is the effective m
51:35 we're gonna make some plots in a is related to the amount of this
51:39 system versus their core system. the difference is again for the
51:47 right? You don't change tortuosity. they should have an exponent of one
51:54 with it. How does the tortuosity ? Nobody objected. When I asked
51:59 to accept that the exponent is related the rate of change of tortuosity with
52:06 . So now I'm validating that for here, right? For individual
52:12 there's absolutely no reason you would expect bugs to change the resistivity in the
52:18 way is changing the matrix velocity. . We're gonna do an exercise.
52:28 how here, if we have multiple systems, we just have to put
52:33 rock together. We start with an of one B of one. We
52:38 that connected four system. First, matrix porosity, we get to whatever
52:43 matrix ferocity value is. And then add the buggy velocity to get to
52:48 final formation. We literally are building rock via individual steps of adding four
52:58 . Is that OK? We will that what happens for it if I
53:05 a fixed matrix property. What happens I add more and more about moving
53:15 direction? For example, more as add the further I add this
53:19 the M value, by the as as was asked is always we
53:23 a point, we draw a line to here. It's the slope of
53:26 line. That's the lambdas are the associated with these individual forces. What's
53:37 to them as I add more and of this slope back here is getting
53:47 and larger. Can I go forever this way? No, because ultimately
53:55 removed all my in inter granular this thing percolates, right connects up
54:01 this thing has to roll back down here, I would add more and
54:08 of a and you actually can see in one of the samples uh where
54:15 happens. And if you look at thin section, the buggy porosity is
54:19 across the entire thin section. And get, in fact, quite a
54:23 M associated with that. This is important picture. Again, you're
54:28 you're gonna do this in a second you. So and so if you
54:34 through and you calculate this, uh have three different exponents associated with this
54:42 this is where people tend to get . You can model all of the
54:46 values uh the M values it, , the MV values are are um
54:54 a fair amount. But if we up the calculated MS versus our measured
55:02 , we actually do reasonably well over fairly broad range. So the argument
55:07 what what have we accomplished in carbonates that we are able to calculate,
55:14 all of the M values in terms three numbers, right? It's inter
55:20 value of 1.9 the bugging value of and micro porosity being that the non
55:26 velocity of something like 1.6. This all you data analytics fans is basically
55:34 test of kind of of our uh this is actually a correlation,
55:39 We are developing correlations between things. you fit all of the data in
55:44 carbonate block catalog, you get these numbers. If you fit only the
55:49 granular, this is the first data I showed you you get this,
55:54 you fit only the mixed which were ones that had both in granular and
56:00 , you get the same numbers and we fit the bugs only, which
56:04 these, we get these three So independent of the data set,
56:09 get the same li exponents, Independent that this is all the
56:16 this data set, this data set this data set are independent of each
56:22 . So the argument is that each these, right? These exponents do
56:27 depend on what else is present, the same numbers. Yeah,
56:33 you're gonna work on this. Um we're gonna look at classics. Um
56:40 it makes sense to do the Now, happy to do that.
56:44 pass it out, turn the lights and then we'll wrap it up with
56:47 argument about classics and permeability. So , I recognize that this gets a
56:53 confusing. This is why we're gonna an exercise ourselves. You're gonna plot
56:58 up and you're gonna infer exponents and like that. What's going on?
57:02 , this is it. Thank So what you're gonna have, you're
57:06 need some log log paper to do . Does anybody have any log log
57:13 left, we need to print If we don't, we need Loglo
57:18 to do that. Yeah. So , I'll, I'll finish introducing the
57:28 while I print it out with. , what you're gonna do is I've
57:32 you several carbonate formations, right? will tell you the porosity changing mechanism
57:38 is different in each of these. I would like you to plot.
57:43 first thing is quite simple. You're supposed to plot total porosity versus formation
57:49 and then measure the sloths that will you the M value. Then what's
57:54 happen is I'm gonna ask you to , I'll go through it with
58:02 This relationship delay, you'll be able see it what the local exponents are
58:09 buggy and matrix ferocity. And we'll that for at least a couple of
58:16 . The rest we can do at and then uh we'll, we can
58:19 about what you find later. So gonna help you get started. And
58:23 , and, and we'll go from . It, it really is less
58:28 than you might think at this Yeah, that's the, so we'll
58:41 a break while he prints the That true. Uh I, the
59:03 thing is the zone and square the and square the log data to get
59:19 I know. So that looks Except that it were because I,
59:23 was, you should calculate a So you're gonna get this. So
59:30 take your re activities and plot Yes, and that's what I did
59:37 them on the, I usually recommend the Ingle flat first. So this
59:42 what I did I do you think were saying that you should be getting
59:56 bulk density? So you should be something like 265 or something you got
60:04 gives the grain density that allows you calculate velocity once I know the grain
60:09 . So this this is fine. , this is fine. They're all
60:14 , right? These are all these three have oil. So it's
60:20 obvious just looking at the reason. . Yeah, because I I thought
60:25 were the ones that I maybe you it right? But this is pretty
60:31 and these all lie on a single and then uh you can get the
60:36 valued for the grain density out of . So this is the thing this
60:42 not for the I understand you Yeah, you don't care. My
60:48 all here. It's better to do . I don't pick a plan.
60:52 extrapolating your resistivity data or your blind to zero ferocity, you're extrapolating it
60:59 infinite resistivity which is zero ferocity. that value of the bulk density will
61:07 zero ferocity will be the grain Now I wanna do the picket clock
61:17 now you can calculate ferocity. I the grain density I can, I
61:21 plot the I can calculate my porosity I can make my picket clock.
61:26 I, yeah, and then you it on paper only part. So
61:38 have the bulk density, you have bulk densities and you can,
61:44 just by plugging in that weighted And then you're gonna assume that your
61:49 are RT. So you're gonna plot , you usually would plot this using
61:57 paper like this. So this is formation factor I would start with just
62:03 help you 0.11 10 and 100 100 one is a decade. So that's
62:19 and 100. And this is a of one ferocity of 0.1 0.01 10%
62:36 calculation. OK. Then this is one that you get the, which
62:43 you M and the intercept will give a hard. And then once
62:52 once I know M I can calculate A. Yeah. Yeah. You
63:07 just then plug into Archie's equation. know RW. So I know I
63:12 RW. Right. So I can the water saturation. These are all
63:32 saturated. So F that's gonna equal over P in inter granular squared and
63:43 your granular over speak with my final . First power. We're gonna use
63:56 to interpret our plots. You can simplify this if you want, it's
64:14 over the granular. Yeah, I you to do it graphically, Miss
64:35 . If you have an extra sheet yesterday. A log, log paper
64:38 can get started. Oh, A couple of people for donuts.
67:42 would, because it varies more It's traditional to do that. You
67:47 more room. It'll sit on the and then, yeah, so you
68:01 put it on one. I I guess they away from each other
68:10 some extent, I get that might you to do them in different
68:44 You were asked to uh find a on a and, or you can't
68:51 a value then that you can plot , it assume M equals and now
68:56 should find saturations, find what the looks like with varying saturation, just
69:03 any point and make it more Like easiest one is M equals N
69:11 two. If I go to 50% , I'm gonna increase the resistivity by
69:16 factor of four, they can take point. You want increase the reason
69:22 should you buy a factor of four it's gotta go through the same
69:26 OK. So you're just gonna get variety of lines with different slopes for
69:31 different saturation. You'd be an expert plotting on log log paper by the
69:53 we're done. Yeah. So how you interpret that formation? I don't
70:15 which particular exercise this is, that's local slope. Sure. And then
70:29 can calculate M for each of these , which is what I'm asking you
70:33 do here. Yeah. It's just a one P one. Yeah.
71:59 . OK. So which core system changing in that one? Both of
72:24 enter the inter particle or the buggy ? Mhm OK. 5 29.
72:38 a of wine. I bought two think. Know. Yeah, he
73:33 . Yeah, it's gonna be I would, I would put my
73:35 here. You plotted you, you RT here. You're plotting the formation
73:41 . That's the difference, right? you're gonna do the same thing you
73:45 F one B of one in the and then this would be 100%
73:52 OK. 10% velocity and then 1% and then an F of one 1000
74:04 for 1 1000 1000 100 100 and plot on that. Yeah, it's
74:30 on this axis, but this would 100% porosity, 10% porosity then
74:49 OK. So what, what was local slope for this first set of
75:07 ? They should wind up quite nicely the way they plotted, right?
75:20 , you'd be better off switching these , by the way, having
75:25 You don't, you don't need, need more decades of resistivity than you
75:29 fro the one just like the other . The, the formation factor is
75:49 vary a lot more than the velocity I know you're better off having three
75:55 for the formation back there just two for crossing, right? So the
76:17 , what people do is they will F equals one equals one here,
76:25 got it right. So this would F equals one P equals one.
76:31 would be so porosity, one porosity 10% porosity of 1% 431 10 and
77:24 . So in, in the you put an F of one B
77:27 one. So when you trad everybody wants to turn it that
77:36 but you, you had it So this would be right, you're
77:44 porosity this way. So why this this way? This would be an
77:47 one fee of one. This would a porosity, 10% porosity, 1%
77:52 factor of 1 10, 100 and . Hm. Yeah. One.
78:58 yeah, it should be this way increasing that way. So, so
79:06 would be F one B of 1 1% porosity and then 1 1000
79:17 And this is a formation factor. not a picket plot. This is
79:22 you have normalized to the brain So ultimately, that plot formation factor
79:29 to equal, equal one and the . Mhm mhm to be nice straight
80:20 . But then you draw the slope those that gives you your lambda.
80:36 I didn't. Mhm Cool. And be an expert. Oh Yeah,
81:19 give me two and none of them this one the old it's not,
81:34 just not the same exercise. I've several versions of this. Right.
81:48 in a different order. So it's be obvious what the answers are.
81:54 all, they're all straight lines on point. Right. And then they're
81:58 have different slopes. And I, just don't remember for this particular
82:03 which it is, it'll be obvious the right answers are if you
82:17 I can even give you a spreadsheet you can plug these numbers in,
82:22 plots yourself if you'd like. Um are, yeah, they,
82:35 these are spreadsheets, right? So can plug whatever numbers you want into
82:39 steps that will generate the answers for . Yeah, let's do the first
83:13 first. So what do we So what's the slow? Yeah,
83:22 run. Just measure it with the pretty close to one to me.
84:12 does that mean? So m is be bugs. So web core system
84:19 changing your buggy process. That's the four systems that's changing gives you a
84:25 of one. What is the So you're supposed to build a model
84:33 , right? Yeah. But what that tell you? And this is
84:50 formation factor plot. If, if was a picket plot, that would
84:55 our w this goes what happens over ? If my, if my total
85:02 is one, what's F equal which is you extrapolating to the total
85:13 being one F is equal to one being total F is equal to one
85:25 B intra granular that tells me what intra granular velocity is. OK.
85:45 I ask you to calculate it for of these points. What my buggy
85:50 is and what my matrix porosity How do I get that?
85:59 We all have graph paper. I take you through the start of this
86:03 a more organized way to do it you're doing it. So everybody label
86:08 axis. Has everybody done that? right. So now I want you
86:12 take and start from F of one of one and draw a line with
86:17 two all the way to the edge the paper. You can, you
86:20 do it on here if you So start there we go one decade
86:25 two decades up and draw a line that point at slope two. So
86:32 start from FF equals 13 equals It's like it's over there.
86:41 better be according to the way you it. This would be 1,
86:52 1000 and this would be again, 0.01. So we go one decade
87:01 two decades up that salt too, ? Everybody see how to do
87:13 Start here. One decade over two up his slope tubed starting here.
87:26 slope two. These are the same . So that's why I can use
87:29 . This is equal to this. slope two is just this and then
87:34 of them, right? Draw that . Everybody got that there.
87:52 well, I'm gonna ask you in second. So you draw all the
87:56 up, then I want you to that line in inter granular porosity.
88:08 ? So what, what, so slope 21 decade over two decades up
88:15 . So you need to go through point to slope two and that point
88:19 slope two. You just draw a all the way up to slope
88:27 Well, yeah, drive all the off. Cool the of the
88:41 So the end with it. And say what? Oh, all right
88:55 everybody labeled that the inter granular porosity ? Yeah. And now you've plotted
89:09 data on there. I guess all you extend that to where it crosses
89:14 other line should have slope one, should cross and that other line with
89:45 one, you should be labeling buggy . Yeah, I think mhm
90:53 Then do my best to show people this. That's the idea. Are
91:04 ready? So let me switch to pen, I can show people you
91:11 look here too as to what we're do. So you need to put
91:31 power behind it, right? You to or we can just mhm Are
91:40 including? Yeah, just copied the one. Yeah. Sure. That's
92:14 . All right. So what, we're gonna do, you can make
92:18 a little bigger. I get rid this stuff here. All right,
92:27 . So what we're gonna do is , 1st of all, we got
92:35 label reacts. This is kind of . So we're gonna insert back
92:41 And this point here is F equals , it equals one like I call
92:49 P at this point. And you're label this, this is, this
92:58 formation factor one. We're gonna put here and we're gonna put the,
93:05 we're gonna put formation factor here. this is F equals one P equals
93:11 . This is a porosity of This is a porosity of 1%.
93:16 is the formation factor of one formation of 10 100 et cetera. This
93:49 after all that happened, doesn't This is Ken, I copied her
93:56 thing. This would be 100 and is 1000 right? Everybody got
94:24 And then my porosity, this is ferocity. This is 10% ferocity.
94:39 will call that 0.1 and then 1% here. 0.01. All right.
94:56 the next thing I asked you to was draw a line with slope two
95:02 here. So that means we're gonna one decade over two decades up.
95:19 gonna start here at F equals one equals one. This is very
95:24 we're gonna go one decade over two up. So we need to go
95:28 that point. I'm gonna make this . I personally like red drama,
95:47 ? So that's my then you're gonna that the inter granular porosity line.
95:55 and called this slope two. If remember was the rate at which formation
96:01 changed with inter granular porosity granular, ? Yeah, I like see
96:37 So we need the bill and we solid bill and gonna make one can
96:46 it, gonna make it white. the inter granular porosity. One,
96:50 . OK? With that. So is how my formation factor will change
96:55 changing inter granular porosity. Everybody understand . Oh yes. Right now,
97:11 we have to do is to add . So you plotted a bunch of
97:14 on here but uh I don't know . Uh well, let's just assume
97:20 I have 10% inter granular porosity, ? So I started here, I
97:25 to 10% into granular porosity and then start to put bugs in that's gonna
97:37 slope one games. So here's slope . And then if we start
97:45 if I start at 10% in a porosity, I would then be moving
97:49 that line. So all of these have the same in inter granular porosity
97:57 easy. I have I have points here any point on here. I
98:01 I as I look at the effect bugs, I would move back to
98:05 to the inter granular porosity I had start at, I start here.
98:11 go to my in granular porosity. I add buggy porosity. So this
98:16 sample, what is it? I put multiple points on here if you
98:24 . They, they, that's how work. That doesn't look like a
98:47 . So you have a, you various points here. I don't know
98:50 you want to label them. Maybe like this. So you have a
98:54 , maybe that lies there. Excuse me, you have a bunch
99:51 points lying there. So how did get to each of these points?
99:55 only way you can move around this . You start here, you put
99:59 granular porosity then bugs. If I to look at the effect of
100:04 I have to go back and see my buggy porosity line crosses my inter
100:09 porosity line. That's the amount of granular porosity I had they can see
100:14 each of these points out of the exercise. I'm gonna get the same
100:17 inter granular porosity. One of these , for example was up here.
100:24 would happen is why I'm having like troubles coping and past and you're the
100:41 making to do this. So I have with the same slope this point
100:47 it was there in this slide This point would have a different the
100:54 porosity. The only way to get is to go up this line to
100:59 in inter granular porosity and then add to get to here. How much
101:04 porosity does this point have? The porosity for this point is like this
101:09 10, 20 about 2025 26%. the buggy and the granular porosity is
101:18 like one to read up here. , about maybe 2.5% something like
101:28 So you can uniquely identify on this . What my in inter granular porosity
101:34 and what my buggy porosity is total is just here this value. But
101:41 granular porosity is this value either right the top or the bottom. And
101:46 porosity is the difference between my total my inter granular porosity. So I'm
101:51 you to do that for each OK. So they all, they
102:06 have the same in inter granular para differing buggy para. So immediately out
102:13 this plot, we see what pore is changing my in inter granular porosity
102:18 constant. My porosity is changing the porosity changing in this horizon. This
102:27 is parts. So all I'm doing had some rock at a constant in
102:31 granular porosity, right? And I'm bugs in it. Yes,
102:37 So I can follow, right. di genesis that's happening here. You
102:45 we did something similar with our Cross plots. Yeah. Right.
103:00 . Are they OK. Sure. was a pitch. You remember the
103:11 when we plotted the samples that had intra granular porosity, they had a
103:16 of about 1.9. So I'm just it too to make them as
103:22 That was, that was bit. it's a typical number for undergraduate pro
103:26 around two. Whereas bugs remember bugs to be one because my tortuosity isn't
103:34 in a bug. So that's gonna slope one, but they are also
103:40 intuitive numbers to get. So you follow basically this same workflow for each
103:51 the lit. They're gonna have a reason for the porosity changing. Then
103:59 ask you, you have the matrix . What does the intercept mean?
104:18 you can see you can read off graph or over there? The equation
104:24 following is on the board over So what happens when my total porosity
104:30 equal to one in the equation on board? F is equal to one
104:36 P inter granular? You can see could see my in inter granular porosity
104:43 was 10%. What's 1/10 percent? . So that was equivalent information.
104:53 intercept here tells you what that inter porosity was, right? Where that
105:27 where they intersect that tell you your a granular porosity and my buggy porosity
105:33 changing can extrapolate this all the way here, right? And what's the
105:39 between that point and that point on board? This extrapolating extrapolating point is
105:51 the total porosity is equal to So F is equal to one over
105:56 inter granular at that point. Oh . So buggy porosity, what I
106:05 is I have my intra granular porosity this point. I have my total
106:09 here. And then I also have closure correction that P total is equal
106:14 P in a granular pro plus P . So all I gotta do is
106:20 my integra my to inter inter granular from my total porosity. That will
106:25 me my lucky. They all have same in granular ferocity and then I
106:37 . Yeah. OK. Absolutely. yeah, questions, confusion,
107:21 So they're gonna do the next one you to figure out. So this
107:34 like a straight forward, right? we had it was just like just
107:37 the real data I plotted. We a constant inter granular porosity and we
107:42 varying bro plot two. Let's see we can figure out. Make the
107:51 for two. You're still gonna make same plot. The under granular porosity
107:56 here has slope two. Then you're plot this data. It's gonna lie
108:00 up here. OK. What's what's slope of this one? The second
108:30 they should lie pretty well on the line again if you're platinum,
108:43 Definitely. Definitely I got. no, it's the same scale as
108:57 . So these are all your Yes, sir. Yeah. Which
109:14 is the one that's long is The same one for both of you
109:22 . Over the last everybody else I get either one or six. Like
109:36 can make it straight here. It's . There's a mistake if we plot
109:47 guys, what's the slope of that should go through there? That's
110:05 uh, it's just your slope. , too. Mhm. Mhm.
110:15 . Yeah. Yeah. Yeah. . Again, just put it as
110:30 you can through these points. I that guy. Let me check and
110:53 move on to three. OK. . Yeah. Mhm. Mhm.
111:22 . Yeah. Yeah. Yeah. . Yeah. OK. OK.
112:03 what? Yeah, there there might a problem with two. Move on
112:13 three and then I'll fix that. . OK. Right. OK.
113:02 . Ok. OK. Yeah. , it always has slope too.
113:43 goes through apple one P one that . Questions thoughts. So basically
114:12 we estimate that the key line. ? And now the total minus that
114:26 that. Yeah. And now the those those back, you know,
114:37 got the same point. Oh, see. Thank you. So II
114:59 know. So then you did the has to be two. So we
115:03 one decade over two decades up or inches, 10 inches or two
115:10 four inches. But it's, it's a measurement. It's not reading
115:17 So it would go through here. you had a soap of two,
115:21 would go through, this is 10% would go through that line versus
115:27 Yeah. Should, should go through . Well. Ok. Yeah,
117:12 , yeah. Yeah. Yeah, fine. Yeah, you should do
119:34 on a linear paper. All So just the relationships between the two
119:44 systems, right? What's, so just do it on linear paper?
119:49 can ask him to get it when comes back. You're just looking for
119:55 the ratio of the two core systems . He can do it in a
120:00 if you want. Mhm OK. , just skip formation two for now
121:24 like figure out what's going on with . Just do the to the other
121:29 two. Mhm. Right. I think what's going on is but
125:22 I would like you to do is worry about that yet. Start
125:27 Yeah, buggy cross versus matrix. do that for sample two.
125:37 Yeah. So all you do is go back to here was one right
125:44 they intersect is inter granular porosity. can use the equation on the board
126:00 you want. Once you're familiar with what happened to get F versus B
126:05 in the inter inter granular porosity you , you have B total. So
126:13 times P total is equal to one P in a granular and I'll give
126:36 a more accurate number. What's happening the third one? This is very
127:01 . OK. I have lots of with it. Exercise. Where,
127:05 do they play pretty. Oh So what does that mean? So
127:13 , if you're going back, what wanna do is go back to this
127:17 that's gonna give you the inter granular . That's an infinite slope, by
127:22 way, not zero. Oh So graphically this is all in the
127:30 this has a little more, a more and more vs No,
127:43 no. This is the only one has granular velocity. It's this one
127:52 because you extrapolate back with slope you always end up with the same
127:56 granular porosity. Here, we have go back with slope one again and
128:01 gonna get more buggy porosity, For each of those, the the
128:11 thing you can do is you really use the on the board is the
128:16 for between formation factor and the different systems. They gave you two and
128:21 that's pretty simple. Formation factor is one over P or granular 10 be
128:26 . I've given you the total you calculate for E and a granular given
128:32 f you can calculate for what that . It, it's better to do
128:36 graphically. It's just a little you should do that for two
128:44 I mean, they, they're it's just that it's a curve
128:47 it's not exactly straight. How are doing? So, right. So
129:09 said yeah, move on to the one can go to this one.
129:21 does three look like, has anybody done that one? Yeah, for
129:26 while. And it's pretty steep, again. Calculates the intra granular porosity
129:34 each of those. Yeah, a too. Yeah. It's a,
129:51 a curve line. They can still . It's that, it's always the
129:59 here between here and here was So it's just, you can see
130:04 happening as your, your huggy process getting bigger as you move up
130:08 Right. Yeah, I OK. that. Yeah. Right. Get
130:52 to the line. The granular right. No. So what's happening
131:07 if you go back to the inter granular line, you're getting more and
131:11 buggy porosity. OK? You still the other side of the better.
131:21 that's a problem. If it's If it's close, then it's just
131:37 in a granular. Yeah. Yeah. That's within air bars.
131:54 Different. Uh uh So again, , you have different, not
131:58 but you have, you have a model for how your porosity are
132:03 So what's happening here? My buggy changing, I have constant inter granular
132:10 would happen? Um If I had line, I could have a line
132:14 my buggy porosity was constant. So distance from this line would be all
132:18 same and my matrix porosity was changing inter granular would be one of the
132:23 examples. And then if you actually one with a the same slope,
132:31 . Again, this, this file is long. I, I should
132:35 something, maybe reprint this and try again. Let him take it at
132:41 . I don't know what happened to . Yeah. Yeah. What
135:15 It's pretty big but we can only 100,000. Just skip that point.
135:22 . It's not gonna help you You could add, you need another
135:27 but you don't have, uh, can do it. So I got
136:32 , I got, I got that , and, and just always the
136:42 between here and F one B So no, no, that,
136:51 , no, that goes between here here. The slope of that line
136:55 M you can see this one is close to two and there M is
136:59 getting bigger to each point. And slope of that line is M the
137:09 GM for the younger ones because they following the same, right? So
137:18 is again getting bigger this so M the slope going back to an one
137:24 one this lambda, right? So is changing this the, when you
137:29 the local. Yeah. So these be getting bigger if we add
137:34 And then this one, what happens uh yeah, my buggy porosity is
137:39 bigger. My matrix porosity is all same. OK. And so that
137:59 on the line. Yeah. So just gradually getting bigger. So we're
138:03 a 1 to 1. Yeah, to the inner granular line. Give
138:09 my, OK. Uh This is elementary question but not. So,
138:14 the, the model here is just , there's a constant total ferocity and
138:19 matrix and buggy porosity are both So we get differing and even though
138:26 though my porosity is the same, what all I'm doing is exchanging matrix
138:33 , but I don't know why I'm even know. How do I make
138:39 I'm doing, you're, you're, doing fine. So it's just you
138:43 , you can just put your ruler below one and then just move it
138:46 parallel to that, right? And get you back and, and the
138:51 thing you can do if you we can just use this is equal
138:56 one over the inter granular times the and giving you this giving you
139:03 you can calculate that. OK. . Rather the first time you do
139:11 graphically just to see what's going I gave you the answer to that
139:17 . All right. OK. Oh God. Yeah, I just
140:18 So that, yeah, so you the same graphics. It's just gonna
140:22 basically a Yeah, I probably should separated that more. It's a vertical
140:29 . The veracity changing yet the M is changing. And why is that
140:34 ? Because the relative amounts of bugging matrix velocity are changing. Both of
140:41 are changing but you're gonna get different because both four systems are changing.
141:12 . Yeah. So, so for two, I'm gonna give you different
141:25 . Well, let's all write these , cross out the existing numbers.
141:29 gonna give you new numbers. So porosity 0.06 and the formation factor is
141:44 . Second one, total porosity 0.1 factor is 100 and 66.7. Third
141:53 total porosity 0.16 formation factor is 100 4.2 total porosity 0.24 formation factor
142:07 And then the last one total porosity formation factors. 55.6 that one somehow
142:16 corrupted somewhere along the line. Sorry get those numbers. You're missing 1.06
142:29 0.166 0.7 0.1 604.2 0.24 69.4. then 0.3 55.6. That's enough.
142:49 sure or just do four of That's five. I'll try one more
142:58 . Ferocity 0.1% ferocity 0.16% 0.24% 1.2 30%. Try again. 6% 10%
143:12 24 and 30. OK. Got five formation factors associated with that 277.8
143:26 0.2. 69.4 55.6 everybody. I don't know what happened to that
143:40 just over the years. It got up. Sorry, that should give
143:51 a nice straight line mentioned. I think I was actually changing the
144:43 and two. Yeah, you could change it and send it back.
145:07 these are all at roughly the same total porosity but they have increasing
145:17 Yeah, you just go back to . I would slope one.
145:21 I would go back with slope one here to get your inner granular
145:26 You're basically on the line and these have increasing. So the point is
145:31 have roughly the same porosity but your porosity is increasing. So even at
145:36 same porosity, you can get multiple factors because the core space is get
145:41 differently. Yeah. But in any , we, we, I
145:45 we assume that it's a in Yeah, we always go soft
145:52 That's the whole point of the whole is that there's an ex exponent associated
145:58 the core system, that's always the and it can cause the GM to
146:03 different values. And this was an , it should have spread the
146:08 If I give it again, I'll that. I, I could have
146:12 had these go further. Yeah. , I I, yeah, that's
146:18 but it, it still illustrates what wanted it to. Yeah, they'll
146:26 buggy here. This is all matrix . Ok. Yes, this is
147:05 long enough, we'll just go to and then we'll go to the other
147:10 . Ok. Yeah, we can that. People can stay and work
147:17 this or do whatever they want. . Uh, general, it depends
147:27 much interest there is. But I suggest we go over there.
147:30 what time is it now? So say 12, you should be back
147:37 one. We should go over Maybe we could go over there at
147:42 . So I'll come back and talk Shay sands here or if there's interest
147:47 can finish this exercise or whatever people to do. So, so we're
147:51 go to lunch now, if you , we just come back in an
147:55 , we'll finish this and maybe do or whatever. Then we'll go for
147:59 lab tour will end, the, end the day over there.
148:12 You know. Yeah. Yeah. . No, we're ready to
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