WEBVTT Kind: captions Language: en 00:00:02.110 --> 00:00:03.719 Okay, good morning, folks. 00:00:03.720 --> 00:00:06.800 Welcome to the Earthquake Science Center seminar. 00:00:06.800 --> 00:00:08.740 Just a quick announcement for next week. 00:00:08.759 --> 00:00:11.160 We’re going to have Dara Goldberg, 00:00:11.160 --> 00:00:15.500 and she’ll be talking about rapid estimation of earthquake magnitudes. 00:00:15.500 --> 00:00:19.800 Today it’s my pleasure to introduce Ingrid Tomac. 00:00:19.800 --> 00:00:24.320 She is currently a professor at UC-San Diego in the department of structural 00:00:24.320 --> 00:00:28.400 engineering, and her background is in geotechnical engineering. 00:00:28.400 --> 00:00:33.370 She graduated with a Ph.D. from Colorado School of Mines, 00:00:33.370 --> 00:00:36.300 and she worked on enhanced geothermal systems – a lot of lab work 00:00:36.300 --> 00:00:41.660 and modeling work in the civil engineering department there. 00:00:41.660 --> 00:00:45.020 So really excited for her talk today. Ingrid, I’ll let you take it away. 00:00:45.020 --> 00:00:46.460 - Okay. 00:00:48.060 --> 00:00:51.980 So, thanks, Jack. And I’m very happy also to be here. 00:00:51.980 --> 00:00:56.340 I have never given a talk at USGS before, and I don’t know many 00:00:56.340 --> 00:01:04.120 people except – oh, yeah, except you. So, yeah, thanks for inviting me, 00:01:04.120 --> 00:01:09.460 and hope that you will like what I would like to tell you. 00:01:09.460 --> 00:01:13.580 So most of this talk is from my Ph.D. 00:01:13.580 --> 00:01:18.030 and a little bit of work that I did afterwards. 00:01:18.030 --> 00:01:23.210 The topic is extracting heat from Earth, which means geothermal energy. 00:01:23.210 --> 00:01:29.820 And I would like to give you some insights into micromechanics 00:01:29.820 --> 00:01:36.600 and micromechanical research that I did and hopefully make – 00:01:36.600 --> 00:01:40.800 I’ll give you something with that – some new insights and some 00:01:40.810 --> 00:01:46.590 new information that may – it may be interesting also for other topics – 00:01:46.590 --> 00:01:49.400 earthquakes and faults. You will see. 00:01:49.400 --> 00:01:54.540 So the presentation outline is here. 00:01:54.549 --> 00:02:02.540 So first I will just briefly make an introduction about EGS and mechanics 00:02:02.540 --> 00:02:06.620 of hydraulic fracturing and then proppant flow and transport. 00:02:06.620 --> 00:02:12.140 I used discrete element modeling for my research during my Ph.D., which is 00:02:12.150 --> 00:02:20.620 most of this presentation. So I will make a brief introduction about DEM. 00:02:20.620 --> 00:02:25.560 And then, concerning this research on micromechanics 00:02:25.560 --> 00:02:31.730 or small-scale particle interactions, I will cover these two topics. 00:02:31.730 --> 00:02:36.180 So let me see how this mouse is going. Yeah. There. 00:02:36.180 --> 00:02:40.900 So particularly fluid lubrication effects on micromechanics of 00:02:40.900 --> 00:02:44.129 particle agglomerations in proppant flow and transport. 00:02:44.129 --> 00:02:49.459 And then the – some work on the hydro- thermo-mechanical rock fracturing. 00:02:49.460 --> 00:03:00.480 So I basically have two separate topics which are part of the EGS research. 00:03:01.520 --> 00:03:06.200 So geothermal energy is used for electricity production. 00:03:06.200 --> 00:03:13.739 Now we have, I think, 16 or so pilot EGS sites all around the world. 00:03:13.739 --> 00:03:17.280 And couple of them are selling electrical energy. 00:03:17.280 --> 00:03:23.300 EGS is interesting because this is enhanced geothermal system, 00:03:23.300 --> 00:03:30.900 which aims to extract geothermal energy from low-permeability rock, 00:03:30.900 --> 00:03:36.300 which gets that enhanced by hydraulic fracturing. 00:03:36.319 --> 00:03:40.640 So the difference – if some of you don’t know what is the difference 00:03:40.640 --> 00:03:47.720 between classical geothermal system and the EGS is that the classical geothermal – 00:03:47.720 --> 00:03:57.230 conventional geothermal systems are placed where this steam is available – 00:03:57.230 --> 00:04:04.300 in faults and geysers, hot springs. So we do have geothermal power plants 00:04:04.300 --> 00:04:10.379 in Iceland and Philippines and so on, which are heavily producing 00:04:10.379 --> 00:04:12.640 electrical energy, but they are targeted – 00:04:12.640 --> 00:04:16.520 placed on a source of steam coming out of the ground. 00:04:16.520 --> 00:04:22.680 So the EGS idea is to place these power plants anywhere on the Earth’s surface 00:04:22.689 --> 00:04:31.129 if we are able to frack the subsurface and efficiently pump the cold fluid of water 00:04:31.129 --> 00:04:37.080 probably down and extract the steam, or combination of steam and hot water. 00:04:38.360 --> 00:04:45.360 Most of these pilot sites are in basement rocks in granite, which is what my Ph.D. 00:04:45.360 --> 00:04:49.140 that was funded by Department of Energy to my adviser was about, 00:04:49.140 --> 00:04:55.180 but now there is also this sedimentary rock initiative, and you may have heard 00:04:55.199 --> 00:05:01.569 about SedHeat initiative. So there are a couple of EGS that are 00:05:01.569 --> 00:05:08.869 also trying to frack sedimentary rocks or shale, which are not that deep. 00:05:08.869 --> 00:05:10.830 So the temperatures are significant. 00:05:10.830 --> 00:05:14.439 The deeper we go, we can have higher one. 00:05:14.439 --> 00:05:20.590 But depths are also 4 or 5 kilometers, so it’s very difficult to drill in the 00:05:20.590 --> 00:05:26.689 hot rock and very difficult to frack it and also very expensive. 00:05:26.689 --> 00:05:36.430 And in situ stresses are high. So this is the map for U.S. where 00:05:36.430 --> 00:05:40.180 you can see the resources at the depth of 10 kilometers. 00:05:40.180 --> 00:05:45.870 So the 300 C or 250 C, we have significant resources that are 00:05:45.870 --> 00:05:52.540 already known, but it’s hard to extract this energy at the moment. 00:05:55.500 --> 00:05:58.360 So the tool to understand some fundamental processes 00:05:58.360 --> 00:06:09.569 is micromechanics and then I looked at some problems, and I got some 00:06:09.569 --> 00:06:14.860 interesting conclusions that I would like to present to you today. 00:06:14.860 --> 00:06:20.040 Most of these topics are hydrothermal chemo-mechanical coupled processes 00:06:20.040 --> 00:06:26.080 in rock during hydraulic fracturing or during extraction of energy. 00:06:26.080 --> 00:06:30.100 So we don’t really know how those processes are coupled. 00:06:30.100 --> 00:06:37.240 Are they just – can we use substitution or adding one process to another? 00:06:37.240 --> 00:06:40.650 Or are they really coupled in a more complex way? 00:06:40.650 --> 00:06:43.990 People are starting this – now there’s a lot. 00:06:43.990 --> 00:06:47.460 Then there is dissolution, precipitation of minerals due to 00:06:47.460 --> 00:06:54.960 hot fluid circulation and other component acoustic emission events. 00:06:54.960 --> 00:07:03.600 We don’t actually know what are sources that cause this AE cloud. 00:07:03.610 --> 00:07:08.139 Is it thermal or mechanical or so – and so on? 00:07:08.139 --> 00:07:10.400 And rock heterogeneities across scales are a problem 00:07:10.400 --> 00:07:14.740 to address and to actually understand what they are. 00:07:14.740 --> 00:07:19.069 And then mechanics of hydraulic fracturing and then flow and 00:07:19.069 --> 00:07:22.809 transport proppants – these are two topics that I’ll talk more about. 00:07:22.809 --> 00:07:30.830 So first, if you are not familiar what this proppant – so proppant 00:07:30.830 --> 00:07:35.659 is a small granular material that props fracture open. 00:07:35.659 --> 00:07:42.490 It is used in oil and gas industry and then inherited from oil and gas into 00:07:42.490 --> 00:07:49.989 geothermal and a little bit abandoned also from current geothermal trends. 00:07:49.989 --> 00:08:00.969 But I am not sure that – you know, that it’s not useful in geothermal. 00:08:00.969 --> 00:08:07.680 So if you look at the horizontal cross-section of idealized fracture here, 00:08:07.680 --> 00:08:12.199 and this is wellbore. We use proppant to keep this 00:08:12.199 --> 00:08:17.469 fracture open after hydraulic fracturing because the rock in situ stresses 00:08:17.469 --> 00:08:21.559 would tend to close the fracture after the pressure decreases 00:08:21.559 --> 00:08:26.909 when the fracturing job is finished. So that’s why we are trying to 00:08:26.909 --> 00:08:37.490 inject sand or different ceramic small particles – medium sand or fine sand. 00:08:37.490 --> 00:08:41.759 Oil and gas industry is trying all different things. 00:08:41.759 --> 00:08:44.839 They’re trying to mix different materials and use 00:08:44.839 --> 00:08:54.860 whatever they think is good to inject into fractures and keep them open. 00:08:54.860 --> 00:08:58.800 This is just a illustration of fracture conductivity 00:08:58.800 --> 00:09:04.150 as a parameter that is relevant for the flow. 00:09:04.150 --> 00:09:07.769 And it depends on the proppant pack permeability and the fracture width. 00:09:07.769 --> 00:09:16.040 So the idealized picture is here, and what I – immediately, 00:09:16.040 --> 00:09:18.800 when I started my research, thought that this is impossible 00:09:18.810 --> 00:09:26.290 to place this proppant in such a nice way into the fracture. 00:09:26.290 --> 00:09:32.860 So if you look at large-scale models – so these models are used to predict 00:09:32.860 --> 00:09:37.589 the whole reservoir – fracture propagation and then also they put 00:09:37.589 --> 00:09:46.110 somehow the proppant into the model, but they use – they are basically 00:09:46.110 --> 00:09:51.160 trying to replace particles and fluid with some non-Newtonian fluid 00:09:51.160 --> 00:09:57.220 and look at how this fluid is flowing in the new idealized fracture. 00:09:57.220 --> 00:10:02.500 So, on the other hand, there is other research – for example, here, 00:10:02.500 --> 00:10:06.810 from Daneshy, is talking about proppant packs that form in a 00:10:06.810 --> 00:10:12.430 narrow fracture and clog the fracture. So this was something that motivated me 00:10:12.430 --> 00:10:18.779 because it looked more physical, and I was thinking that these particles 00:10:18.779 --> 00:10:24.790 must be clogging rather than flowing freely, nicely into the fracture, 00:10:24.790 --> 00:10:30.329 like replacing dense non-Newtonian fluid. 00:10:30.329 --> 00:10:34.600 Then I looked at some other research, 00:10:34.600 --> 00:10:38.420 which is outside of this oil and gas and proppant area. 00:10:38.420 --> 00:10:44.840 So there is this reference here – a book by Crowe and Tsuji from Japan 00:10:44.840 --> 00:10:50.440 where they look at multiphase flows of droplets and particles and so on, 00:10:50.440 --> 00:10:56.960 and they have one chapter on flow and transport of fluids and hard particles. 00:10:56.960 --> 00:11:02.720 And they say, okay, at the dense-phase flows with high particle concentrations, 00:11:02.720 --> 00:11:05.910 inter-particle forces dominate over hydrodynamic forces. 00:11:05.910 --> 00:11:12.149 So the particle-particle interactions are frequent, and they are – particles are 00:11:12.149 --> 00:11:16.860 kicking each other while they are transported into some constrained 00:11:16.860 --> 00:11:25.340 fracture, which then affects both fluid flow and particle flow. 00:11:25.340 --> 00:11:30.730 And hydrodynamic forces means that fluid is not dominant, 00:11:30.730 --> 00:11:37.410 as you can see here. So interestingly, oil and gas industry 00:11:37.410 --> 00:11:41.149 would always try to put this high particle concentration as they can 00:11:41.149 --> 00:11:46.129 into fracture because they need more particles to prop these fractures open. 00:11:46.129 --> 00:11:51.160 But then it’s a question, how can we model and understand this flow 00:11:51.160 --> 00:11:56.529 and transport, which, in this book, was small chapter, and in the end, 00:11:56.529 --> 00:11:59.240 says it’s not well-understood, the dense-phase flows. 00:11:59.240 --> 00:12:01.920 So not well-understood. 00:12:01.920 --> 00:12:06.400 Another area that I’m looking into now is the sediment transport. 00:12:06.400 --> 00:12:12.200 So people are looking at, you know, river and lakes and sediment transport. 00:12:12.209 --> 00:12:19.410 So this is similar, but again, in sediment transport, we have a big, open fluid 00:12:19.410 --> 00:12:26.290 domain, and here we have a narrow and branch fractures and so on. 00:12:26.290 --> 00:12:28.700 So that’s motivation. 00:12:28.700 --> 00:12:34.019 Discrete element method – it’s very different from finite element method. 00:12:34.019 --> 00:12:39.769 I see that most people are engineers and civil engineers are now 00:12:39.769 --> 00:12:43.459 very familiar with finite element. It start in undergrad. 00:12:43.460 --> 00:12:46.960 So DEM is completely different. 00:12:46.960 --> 00:12:58.500 DEM is a assembly of single particles, and then we use finite differences – 00:12:58.500 --> 00:13:07.720 explicit finite difference to follow each particle motion and then velocity, 00:13:07.720 --> 00:13:13.500 acceleration, force, and contact forces in a time-stepping procedure. 00:13:13.500 --> 00:13:18.389 And time-step is very small. So not only that we can now look at 00:13:18.389 --> 00:13:24.480 the granular assembly – or, granular flow of particles like this, which is just 00:13:24.480 --> 00:13:30.389 pouring sand or something like this, but we can also bond those particles 00:13:30.389 --> 00:13:36.290 and glue them together with the cement – with another contact logic. 00:13:36.290 --> 00:13:42.829 And then model rocks or other solids, and then we can observe directly 00:13:42.829 --> 00:13:49.499 fracture from the large fracture to some damaged micro-crack and so on. 00:13:49.499 --> 00:13:57.850 So this is a time-stepping scheme based on the finite differences. 00:13:57.850 --> 00:14:01.589 Now it’s coupled with computational fluid dynamics. 00:14:01.589 --> 00:14:10.020 Also here, so that we can look at actually the fluid and particle interactions. 00:14:10.020 --> 00:14:20.379 So the CFD is computational fluid dynamics of the fluid field – 00:14:20.379 --> 00:14:31.459 fluid flow field is discretized here over those fixed – over the fixed mesh. 00:14:31.459 --> 00:14:37.399 And then we have the outside layer for boundary conditions. 00:14:37.399 --> 00:14:43.059 And then the particles – here are the DEM, so these codes are coupled, 00:14:43.059 --> 00:14:48.019 and each time-step, they are communicating. 00:14:48.019 --> 00:14:52.690 So the particle motion affects fluid motion. 00:14:52.690 --> 00:14:58.230 And the next time-step, there is some averaging of the fluid flow field 00:14:58.230 --> 00:15:04.759 over the rectangle, or the mesh, and then, of course, if we have several particles 00:15:04.759 --> 00:15:08.329 in the mesh, this is also going to be a little bit average. 00:15:08.329 --> 00:15:13.899 But then the fluid is pushing particles, but particles are also pushing out fluid. 00:15:13.900 --> 00:15:15.820 So it’s a two-way coupled. 00:15:15.820 --> 00:15:21.080 And there are several codes that are already have this kind of coupling. 00:15:21.080 --> 00:15:25.800 So it’s not something that I did or needs to be developed. 00:15:25.800 --> 00:15:32.400 It’s good because we can see what is happening with individual particles, 00:15:32.410 --> 00:15:36.259 and we can see what’s happening with the fluid. 00:15:36.259 --> 00:15:41.050 And then this research objective here was to investigate how 00:15:41.050 --> 00:15:45.920 fluid viscosity and proppant concentration affect proppant settling, 00:15:45.920 --> 00:15:49.740 horizontal flow and transport in narrow and rough fractures. 00:15:49.740 --> 00:15:55.769 So that was my Ph.D., and I’m still continuing this work now. 00:15:55.769 --> 00:16:01.269 So what was missing – and I actually recognized that something was wrong, 00:16:01.269 --> 00:16:08.180 and I will show you some results later, was this fluid lubrication. 00:16:08.180 --> 00:16:14.540 So I, again, actually ran a couple of codes like this, 00:16:14.540 --> 00:16:23.209 and it gave me very unrealistic results because, in literature, we can see that 00:16:23.209 --> 00:16:28.709 the most we can feed into the narrow fracture is 50 or 60% of 00:16:28.709 --> 00:16:32.949 volumetric concentration of particles. And with the classical DEM-CFD 00:16:32.949 --> 00:16:40.430 scheme, I could fit in 90% almost. And everything flowing nicely. 00:16:40.430 --> 00:16:44.910 So I looked at and found this lubrication theory. 00:16:44.910 --> 00:16:52.899 So this theory was developed by Davis, who is – was or is dean at 00:16:52.900 --> 00:16:55.500 UC-Boulder – actually mechanical engineering. 00:16:55.500 --> 00:17:00.170 They looked at the contact of two particles in viscous fluid. 00:17:00.170 --> 00:17:09.159 So if we talk about lubrication, you can maybe know from some bridge 00:17:09.160 --> 00:17:15.560 engineering or mechanical engineering that we lubricate bearings with oil. 00:17:16.420 --> 00:17:18.959 Do you – do you have the idea what that means? 00:17:18.959 --> 00:17:26.360 So like bearings in – steel bearings, if they are completely in a closed 00:17:26.360 --> 00:17:31.080 chamber with high viscosity oil, they will not touch each other 00:17:31.080 --> 00:17:33.330 no matter how big force you are applying. 00:17:33.330 --> 00:17:36.659 And this is what is used in all type of bridge bearings. 00:17:36.660 --> 00:17:45.340 So why? Because of this thin layer of the viscous fluid that prevents contact of – 00:17:45.340 --> 00:17:49.060 now particles, but steel bearings, for example, which push – 00:17:49.060 --> 00:17:53.690 which are pushed towards each other. So this dissipates their kinetic energy. 00:17:53.690 --> 00:17:59.860 And there is a formula for this here. So I said, okay, I want to put this 00:17:59.860 --> 00:18:05.820 formula into my DEM and see, are my particles going to – I wanted to 00:18:05.820 --> 00:18:10.409 try to model better these particle-particle interactions, basically. 00:18:10.409 --> 00:18:23.220 So it is possible to put it in DEM by – so here it’s – it shows the idea 00:18:23.220 --> 00:18:28.980 that actually I modeled around the real DEM particle. 00:18:28.980 --> 00:18:35.070 I modeled apparent radius. So I estimated some distance 00:18:35.070 --> 00:18:40.970 where this lubrication force may start being important. 00:18:40.970 --> 00:18:46.480 And when these radii touched in a time-stepping scheme, 00:18:46.480 --> 00:18:51.529 then lubrication force was basically activated, and it started to dissipate 00:18:51.529 --> 00:18:57.929 any kinetic energy of velocity of those two approaching particles. 00:18:57.929 --> 00:19:02.899 The model is also validated here. 00:19:02.899 --> 00:19:09.260 So this is the restitution coefficient, which is normalized. 00:19:09.260 --> 00:19:13.960 So this is the coefficient of restitution, and this is the collision Stokes number. 00:19:13.960 --> 00:19:23.760 So the Stokes number already contains mass and radius of particle 00:19:23.760 --> 00:19:28.420 and the fluid dynamic viscosity, so it’s the Newtonian fluid. 00:19:28.420 --> 00:19:33.860 What you can see here is basically that the contact behavior – 00:19:33.870 --> 00:19:39.160 so the contact behavior of two elastic dry particles is going to be linear. 00:19:39.160 --> 00:19:43.780 And it can be easily modeled with this Kelvin-Voigt or spring-dashpot model, 00:19:43.780 --> 00:19:48.950 where, if you – if you drop a ball – like, a little rubber ball that you can have at 00:19:48.950 --> 00:19:54.510 home for your kids or dog or something, the ball is going to – you drop – 00:19:54.510 --> 00:19:56.720 you will drop the ball from certain height, 00:19:56.720 --> 00:19:59.570 and it’s going to rebound to some height. 00:19:59.570 --> 00:20:05.060 So this rebound height for elastic materials is basically always the same. 00:20:05.060 --> 00:20:12.510 So now, with this lubrication model, we can see that, if we drop the ball from 00:20:12.510 --> 00:20:18.600 a small height, it will stay on the ground. Because this kinetic energy is going to 00:20:18.600 --> 00:20:24.310 completely be dissipated by the lubrication, the thin layer of fluid. 00:20:24.310 --> 00:20:29.710 And then, if we have higher velocity of the collision, there will be some rebound. 00:20:29.710 --> 00:20:31.870 And this rebound is going to be nonlinear. 00:20:31.870 --> 00:20:37.110 So it’s nice that the experimental validation, 00:20:37.110 --> 00:20:44.710 or some different material spheres in viscous fluid was also done by – 00:20:44.710 --> 00:20:52.059 done by the group that developed Davis and his students and some other people. 00:20:52.059 --> 00:20:54.780 And I was able to replicate this in the model. 00:20:54.780 --> 00:21:06.559 So there is a lag here that is this rebound is not completely matching. 00:21:06.559 --> 00:21:14.149 But the nonlinear behavior is matching. So I went forward with this model. 00:21:14.149 --> 00:21:20.990 So now I had a better tool to look at if particles are going to agglomerate 00:21:20.990 --> 00:21:25.460 or not in viscous fluid based on the injection rate of the proppant 00:21:25.460 --> 00:21:30.169 and based on the particle properties and how frequent they contact. 00:21:30.169 --> 00:21:34.440 So you can see here, this first attempt gave me a bit – 00:21:34.440 --> 00:21:40.429 a spring-dashpot model in DEM gave me this super-high packing for a particle. 00:21:40.429 --> 00:21:45.980 And this is 2-millimeter opening. 00:21:45.980 --> 00:21:53.260 And that’s 20/40 mesh sand, so this is 0.6 diameter sand. 00:21:53.260 --> 00:21:57.799 So with the lubrication contact model, 00:21:57.799 --> 00:22:01.970 I got something more like this – more agglomerations 00:22:01.970 --> 00:22:11.970 and more realistic maximum possible initial packing into the particles. 00:22:11.970 --> 00:22:17.000 So this is – okay, for 4-millimeter channel, so I published this work. 00:22:17.000 --> 00:22:23.380 So from here forward, then I could do modeling to better understand 00:22:23.380 --> 00:22:31.260 what is the effect of fluid motion – what is – so this is the initial 00:22:31.260 --> 00:22:34.970 concentration where I was fitting in here some initial 00:22:34.970 --> 00:22:38.750 particle volumetric concentration. And then looking at the pressure 00:22:38.750 --> 00:22:44.899 difference in some length of the channel – the different channel 00:22:44.899 --> 00:22:49.830 apertures – and see what is going on. So we can see here, for example, 00:22:49.830 --> 00:22:54.830 extreme case – low pressure and high concentration in a medium 00:22:54.830 --> 00:22:57.899 of the observed span of the fluid. 00:22:57.899 --> 00:23:08.450 So I went from water, which is 0.001 to 0.05 fluid viscosity. 00:23:08.450 --> 00:23:15.020 So over here, we can see grouping of particles relatively close to the entrance. 00:23:15.020 --> 00:23:21.399 Some sparse groups are following here. And then logically, the fluid velocities 00:23:21.399 --> 00:23:25.190 are higher here, and the fluid will just go around. 00:23:25.190 --> 00:23:31.799 So in here, I got clogged the channel without any flow inside. 00:23:31.799 --> 00:23:35.210 So this is low pressure and high concentration in a 00:23:35.210 --> 00:23:40.450 even higher fluid viscosity. So I did not have enough energy – 00:23:40.450 --> 00:23:46.139 enough hydrodynamic forces in the fluid – enough pressure 00:23:46.139 --> 00:23:51.860 difference to transport those particles in the channel. 00:23:51.860 --> 00:23:54.399 So this is effect of pressure and fluid viscosity on 00:23:54.399 --> 00:23:57.240 particles agglomeration in 4-millimeter channel. 00:23:57.240 --> 00:24:02.700 So definitely, I could observe and evaluate in the model 00:24:02.700 --> 00:24:09.440 with whatever the model constraints are, now they are agglomerations. 00:24:09.440 --> 00:24:14.429 The other thing that I did is to look at the particle settling. 00:24:14.429 --> 00:24:18.169 I had 2D model, so I looked at the horizontal flow and transport 00:24:18.169 --> 00:24:23.929 and then the settling. So the settling, it also – some references 00:24:23.929 --> 00:24:31.800 say, if we have Newtonian fluids, two particles that are just let fall next 00:24:31.800 --> 00:24:37.300 to each other in quiescent Newtonian fluid will just go apart from each other. 00:24:38.140 --> 00:24:45.360 That’s relatively old, and it’s even older theories here. 00:24:45.360 --> 00:24:49.450 So I tried to see in PFC with my model what is going on, and indeed, 00:24:49.450 --> 00:24:56.600 the particles are going to fall apart in Newtonian fluid if I have a big – 00:24:56.600 --> 00:25:00.510 you know, the big – of water. Not a constrained space. 00:25:00.510 --> 00:25:05.290 So in fracture, of course, is something completely different 00:25:05.290 --> 00:25:10.950 going on because particles are falling into the fractures. 00:25:10.950 --> 00:25:15.909 So I was dropping particles now in a quiescent fluid into narrow 00:25:15.909 --> 00:25:21.860 fracture with different widths with 20/40 mesh sand. 00:25:21.860 --> 00:25:27.220 And they would really form some grapes and channels 00:25:27.220 --> 00:25:32.460 and agglomerate. So I put the rough fracture wall 00:25:32.460 --> 00:25:38.899 in this case to study the fracture roughness a little bit. 00:25:38.899 --> 00:25:45.019 Also, I could see – and this was also not – 00:25:45.019 --> 00:25:48.460 there was not enough attention given to this phenomenon, 00:25:48.460 --> 00:25:55.679 in particular papers from oil and gas that actually, if our proppant is going down, 00:25:55.679 --> 00:25:57.750 the fluid is going to have to go somewhere. 00:25:57.750 --> 00:26:01.650 It’s a closed fracture, especially in a – you know, it has some certain width. 00:26:01.650 --> 00:26:07.669 So if proppant is going to try to settle down due to gravity, 00:26:07.669 --> 00:26:12.350 if the density are different, which typically are, 00:26:12.350 --> 00:26:15.100 between proppant and fluids. But then fluid is going to go up. 00:26:15.100 --> 00:26:19.559 So this upward motion of fluid was even making it worse. 00:26:19.559 --> 00:26:24.740 Fluid would try to find a way and push particles together even more, 00:26:24.740 --> 00:26:29.090 so particles were even more coming into contact 00:26:29.090 --> 00:26:32.960 and then getting into agglomerations and jammed. 00:26:32.960 --> 00:26:37.200 So then the agglomerate forms like this a little bit larger. 00:26:37.200 --> 00:26:40.320 This would act, for a certain amount of time, 00:26:40.330 --> 00:26:44.320 as a big particle and start to fall faster. Then it will fall apart. 00:26:44.320 --> 00:26:51.990 So it’s very interesting to me to look into detail actually what is going on. 00:26:51.990 --> 00:26:59.350 So I think it’s really much different than what we are now – the modelers 00:26:59.350 --> 00:27:07.460 now have a chance to put into their large- scale models for hydraulic fracturing. 00:27:07.460 --> 00:27:10.290 And we don’t really know what are those conditions 00:27:10.290 --> 00:27:12.960 that will cram the fracture. 00:27:13.780 --> 00:27:16.000 Okay, so I don’t know what happened here. 00:27:16.000 --> 00:27:24.510 Okay, so yes, so this is – these are results from number of simulations. 00:27:24.510 --> 00:27:32.520 And here I compared my numerical results with some previously published 00:27:32.520 --> 00:27:37.720 experimental relationships that were done in slots in the lab, 00:27:37.730 --> 00:27:43.039 but wider slots – not narrow slots. So something that represents a main 00:27:43.039 --> 00:27:49.889 fracture of 4 or 10 centimeters wide – not that narrow part of the fracture. 00:27:49.889 --> 00:27:53.880 And I’m also interested in what is going on if the fracture starts to branch. 00:27:53.880 --> 00:27:56.120 Because branch is not going to be very wide. 00:27:56.120 --> 00:27:59.509 So here is proppant volumetric concentration 00:27:59.509 --> 00:28:02.990 versus average proppant settling velocity. 00:28:02.990 --> 00:28:12.330 So I grouped these graphs so that you can see it in a higher fluid viscosity. 00:28:12.330 --> 00:28:19.279 My settling velocities were higher. And then, when proppant concentration 00:28:19.279 --> 00:28:25.020 was increasing, if there was no agglomeration and forming of those 00:28:25.020 --> 00:28:31.340 clumps that fall faster, the whole slurry – if the slurry is homogeneous, the whole 00:28:31.340 --> 00:28:37.759 slurry would settle a little bit slower. But if the slurry is not homogeneous, 00:28:37.759 --> 00:28:43.769 and due to those agglomerates that are forming, the average settling is 00:28:43.769 --> 00:28:49.620 a little bit higher. So that’s just the understanding on what is going on. 00:28:49.620 --> 00:28:55.370 So neither lines are a perfect reflection of reality because these are 00:28:55.370 --> 00:29:03.019 just experimental – limited experimental studies in some certain type of sand 00:29:03.019 --> 00:29:07.650 in some certain bit of slots and bits of fluids, and these are my miracle 00:29:07.650 --> 00:29:15.070 models that also have numerous uncertainties, as any model has. 00:29:15.070 --> 00:29:19.980 So I – with my students at the UC – the master’s student, we looked at a 00:29:19.980 --> 00:29:26.149 little bit how to build some experiments. So we went – we took plexiglass plates, 00:29:26.149 --> 00:29:33.980 and we made a small slot, and then look at the settling of sand in those slots. 00:29:34.700 --> 00:29:38.019 Let me see – it just went away. 00:29:38.019 --> 00:29:42.710 So we look at 20/40 mesh sand – same as in the models, 00:29:42.710 --> 00:29:47.630 and then we also 3D printed the rough fracture that I got from 00:29:47.630 --> 00:29:51.299 [inaudible] in Germany who scanned their rock surface 00:29:51.300 --> 00:29:55.300 of their hydraulic fracturing experiment in the lab. 00:29:57.570 --> 00:30:01.620 So we look at the 2-millimeter-wide slot with smooth cell and then 00:30:01.620 --> 00:30:07.509 with 3D printed fracture. 20/40 mesh sand. 00:30:07.509 --> 00:30:12.690 And then 50, 75, and 85% glycerol water solution, 00:30:12.690 --> 00:30:16.010 which gives us a high-viscosity Newtonian fluid. 00:30:16.010 --> 00:30:23.340 So glycertol is safe. We use it in hand creams and so on, and it’s a stable fluid. 00:30:23.340 --> 00:30:27.110 In industry, non-Newtonian fluids are used more than Newtonian fluids, 00:30:27.110 --> 00:30:30.940 but then we used the Newtonian fluid in the lab to study 00:30:30.940 --> 00:30:35.600 particularly the effect of fluid dynamic viscosity. 00:30:35.600 --> 00:30:44.140 So similar trend is – at least I can say trend is observed in the – in the lab. 00:30:44.149 --> 00:30:48.139 So with lower-viscosity fluid, the slurry – settling slurry was 00:30:48.139 --> 00:30:55.559 more homogeneous, while in glycerol, which is extremely high-viscosity fluid, 00:30:55.559 --> 00:31:00.389 there are those agglomerates and grapes, so to say, 00:31:00.389 --> 00:31:05.280 of particles flowing down. The agglomerates are falling faster 00:31:05.280 --> 00:31:08.230 than single particles around them. And then the fluid is 00:31:08.230 --> 00:31:13.059 also going upwards. So we get this channel type of settling. 00:31:13.059 --> 00:31:19.980 This is, I would say, very different. If you want to model it with some – 00:31:19.980 --> 00:31:25.289 maybe you can model this one with saying that’s a homogeneous slurry. 00:31:25.289 --> 00:31:30.649 But here it’s not, so I think it’s a challenge 00:31:30.649 --> 00:31:33.760 to understand what is going on. 00:31:33.760 --> 00:31:40.400 So the – to better look at the settling velocities, you can use 00:31:40.400 --> 00:31:44.929 the particle image velocimetry. So this is the velocity-measuring 00:31:44.929 --> 00:31:49.679 procedure developed in the field of fluid mechanics and also extended 00:31:49.679 --> 00:31:58.889 to geomechanics or particle mechanics by some [inaudible], who is 00:31:58.889 --> 00:32:01.409 a professor at Queens University now. 00:32:01.409 --> 00:32:09.710 So we took videos and then compared frames, look at the – 00:32:09.710 --> 00:32:15.379 some fractures and then get some average velocities in those batches. 00:32:15.379 --> 00:32:19.450 So my student did a lot of analysis, and here are some results. 00:32:19.450 --> 00:32:26.210 So also – now, we confirmed – of course, when the particle size increases, 00:32:26.210 --> 00:32:29.700 the settling velocity would increase even if you look at just the Stokes 00:32:29.700 --> 00:32:36.059 settling velocity, but then the average velocity of the slurry, what is going on 00:32:36.059 --> 00:32:40.649 with the average velocity of the slurry if we have agglomeration of particles. 00:32:40.649 --> 00:32:48.020 So my student kind of looked at the – and counted those agglomerates 00:32:48.020 --> 00:32:52.779 as good as she could. And came up with some graphs. 00:32:52.779 --> 00:32:57.690 So you can see here, for example, this is lower and this is higher 00:32:57.690 --> 00:33:03.440 fluid dynamic viscosity. So here is the average settling in the lab, 00:33:03.440 --> 00:33:09.230 and then this is settling of some individual particles in this particular – 00:33:09.230 --> 00:33:16.120 same experiment, and this is the settling of some agglomerates that she found. 00:33:17.009 --> 00:33:22.799 So we can see how the agglomerates have more and more effect 00:33:22.799 --> 00:33:28.080 as the glyercol-water solution is increasing. 00:33:28.080 --> 00:33:33.860 So it’s also – like, overall settling is slower in higher fluid viscosities, 00:33:33.860 --> 00:33:38.590 but we have more forming of agglomerates. This is what we found. 00:33:38.590 --> 00:33:43.190 They are due to particle-particle interactions. 00:33:43.190 --> 00:33:47.009 So particles have to come into close contact and then, because this 00:33:47.009 --> 00:33:53.370 lubrication is dissipating their energy, they don’t rebound – re-bounce. 00:33:53.370 --> 00:33:57.340 They stay together and start to fall together in the fluid. 00:33:57.340 --> 00:34:01.899 Fluid goes around them. And they do fall apart again. 00:34:03.340 --> 00:34:10.340 Here, again, this is a comparison of our experimental results now with 00:34:10.340 --> 00:34:17.290 the same formulas that I showed a little bit before in modeling that 00:34:17.290 --> 00:34:22.360 are used now in oil and gas industry. So here, for example, 00:34:22.360 --> 00:34:30.680 in a 50% glycerol-water solution, we see that around 0.4 volumetric – 00:34:30.680 --> 00:34:37.810 initial volumetric concentration, our experimental line is crossing these lines. 00:34:37.810 --> 00:34:43.910 So at a little bit higher fluid viscosities, we need a lower initial concentration 00:34:43.910 --> 00:34:52.230 to get opposite effect – to get higher settling and higher effect of those 00:34:52.230 --> 00:34:55.240 agglomerates that they are forming. 00:34:55.240 --> 00:34:59.540 So we found that increasing of particle concentration promotes agglomeration 00:34:59.540 --> 00:35:06.240 and the fluid lubrication effect on colliding particle-particle interactions. 00:35:09.680 --> 00:35:16.380 So the fluid viscosity is – so we found that the fluid viscosity 00:35:16.380 --> 00:35:23.220 is promoting agglomerations, and then this can be a big problem 00:35:23.220 --> 00:35:27.420 if the – even narrow section of a fracture occurs. 00:35:27.420 --> 00:35:31.890 Because fractures are not smooth and the same width 00:35:31.890 --> 00:35:35.380 over 100 meters of our reservoir. 00:35:35.380 --> 00:35:39.870 But, on the other hand, high-viscosity fluids are used more 00:35:39.870 --> 00:35:46.300 because then there is less settling. So far, they are trying to use 00:35:46.300 --> 00:35:50.540 high-viscosity fluids because they do not have a lot of settling in practice, 00:35:50.540 --> 00:35:54.690 but they’re not – nobody is paying attention to the agglomerations 00:35:54.690 --> 00:35:59.770 and clogging of fractures due to these high-viscosity fluids 00:35:59.770 --> 00:36:04.420 that I suspect is happening. And when I talk to oil and gas experts 00:36:04.420 --> 00:36:08.040 in conferences, they are telling me incredible things – 00:36:08.040 --> 00:36:14.760 something like, oh, so, like, 60% of our frack jobs don’t produce. 00:36:14.760 --> 00:36:18.600 Something like this. They obviously have a lot of 00:36:18.610 --> 00:36:24.100 freedom and space and – because the prices and money is big in the industry. 00:36:24.100 --> 00:36:29.430 And maybe it’s because they’re clogging their fractures right away with proppant. 00:36:29.430 --> 00:36:35.240 So I got NSF grant on this topic – multi-physics models for proppant 00:36:35.240 --> 00:36:41.480 placement in energy georeservoirs. And we are continuing now with the work. 00:36:41.480 --> 00:36:45.320 The co-PI Professor Tartakovsky is now in Stanford. 00:36:45.320 --> 00:36:49.850 Actually, he has background in mathematics, so I hope that he will 00:36:49.850 --> 00:36:56.620 come up with some neat formulas and theories based on our experiment 00:36:56.620 --> 00:36:59.740 and extensive modeling that my student’s going to do. 00:36:59.740 --> 00:37:02.500 So he has [inaudible] task in the end. 00:37:02.500 --> 00:37:08.910 Okay, so this is about the first part of the talk, and then I have the 00:37:08.910 --> 00:37:12.320 second part that is more rock – maybe more interesting for you? 00:37:12.320 --> 00:37:15.430 Or for you, Jack? I don’t know. 00:37:15.430 --> 00:37:17.860 So these are the research needs and questions. 00:37:17.860 --> 00:37:23.330 So what are the future proppant – what are the proppant interactions 00:37:23.330 --> 00:37:26.750 for realistic fractures? How do we prove proppant placement 00:37:26.750 --> 00:37:31.950 design or perfect fluids – proppant characteristics. 00:37:31.950 --> 00:37:36.210 And then, we don’t know how the fracture surface looks. 00:37:36.210 --> 00:37:39.830 And the – we have theis experimental plan on a large-scale facility. 00:37:39.830 --> 00:37:47.100 So this is basically the grant work, more or less. 00:37:47.100 --> 00:37:52.410 So the other micromechanic study that I did for my Ph.D. 00:37:52.410 --> 00:37:56.710 is this – related to hydraulic fracturing. 00:37:56.710 --> 00:38:04.130 So, in short, also now we have, on one side, a wellbore and then some idealized 00:38:04.130 --> 00:38:13.900 model for fracture propagation in rock, which relies on fracture mechanics or 00:38:13.900 --> 00:38:20.640 linear elastic fracture mechanics with Mode I or II or III fracture openings. 00:38:22.760 --> 00:38:31.500 We rely also on elastic behavior and tensile fracture or 00:38:31.500 --> 00:38:36.340 Kirsch’s solution at the wellbore to initiate fracture. 00:38:36.340 --> 00:38:43.960 This fracture initiation formulas for the Kirsch’s solution can be modeled also 00:38:43.960 --> 00:38:48.510 using poroelasticity or thermal stresses, which we have in geothermal reservoir. 00:38:48.510 --> 00:38:52.600 So this is some theory behind – so there is a temperature difference 00:38:52.600 --> 00:39:00.400 between fracturing fluid and host rock. In geothermal, this temperature can 00:39:00.400 --> 00:39:07.320 be significant enough to cause stresses and damage, which I will show. 00:39:07.320 --> 00:39:12.760 And then what – I also looked at – this is strain rate effects. 00:39:12.760 --> 00:39:18.270 So for example, I was able to pull out some research from before, 00:39:18.270 --> 00:39:24.030 and we can see here that the – both energy absorption or 00:39:24.030 --> 00:39:31.270 compressive strength or also fracture toughness increases if we 00:39:31.270 --> 00:39:38.560 have increased strain rate loading. So with earthquakes or blast here – 00:39:38.560 --> 00:39:44.140 or, in other words, if we – if we are trying to induce a single, 00:39:44.140 --> 00:39:51.820 nice hydraulic fracture, we need very low quasi-static loading rate. 00:39:51.820 --> 00:40:00.781 If we are increasing the loading rate, we will get this type of – you know, more 00:40:00.781 --> 00:40:08.070 what would the blast do – a fragmentation of rock at higher forces that are needed. 00:40:08.070 --> 00:40:14.720 So you will see – I’m showing this now because I saw some interesting 00:40:14.720 --> 00:40:23.300 effects in my – the modeling, which is not saying that we are using high rate, 00:40:23.300 --> 00:40:29.760 but we do have a consequence that looks more like this than like this for modeling. 00:40:29.760 --> 00:40:33.150 So that’s the fracture toughness – the static and dynamic. 00:40:33.150 --> 00:40:39.900 So these are the lab tests that are available for different types of rocks. 00:40:39.900 --> 00:40:47.140 And then we have this cloud of microseismicity for reservoirs, 00:40:47.140 --> 00:40:51.900 which is not well-understood. We don’t know which circle is here – 00:40:51.900 --> 00:40:55.010 fracture, which circle is damage, what is going on. 00:40:55.010 --> 00:40:58.030 So also, Jack, you are working on this. 00:40:58.030 --> 00:41:01.400 So many, many people are trying to understand how can we 00:41:01.400 --> 00:41:06.360 better interpret acoustic emission results to get more knowledge about fracture. 00:41:06.360 --> 00:41:08.780 Do we have a fracture or not? 00:41:08.780 --> 00:41:12.180 So there’s a problem in georeservoirs. 00:41:13.680 --> 00:41:19.980 Luke Frash in our research group did some lab work. 00:41:19.980 --> 00:41:25.590 Also they observed the cloud of acoustic emission in granite. 00:41:25.590 --> 00:41:30.840 And then also, when we looked at fractures in rock mass, 00:41:30.840 --> 00:41:37.920 we can see that those fractures are really not very smooth and nice. 00:41:37.920 --> 00:41:41.100 So this refers to both proppant flow and transport 00:41:41.100 --> 00:41:46.640 and then fracturing micromechanics research. 00:41:46.640 --> 00:41:50.860 I don’t know – tell you a little bit about the model. 00:41:50.860 --> 00:41:56.380 And then show a couple of results for fracturing – 00:41:56.380 --> 00:42:02.060 share with you some conclusions, and that’s going to be it. 00:42:02.070 --> 00:42:07.280 So I mentioned that, in discrete element model, we can actually model solids. 00:42:07.280 --> 00:42:15.710 So this is the way to couple solid fluid interactions but also first to say, yes, 00:42:15.710 --> 00:42:20.790 we can bond those two particles with the cement bond, which can transfer 00:42:20.790 --> 00:42:24.670 forces and bending moments from one particle to another. 00:42:24.670 --> 00:42:28.510 And then we can actually observe this bond to be broken. 00:42:28.510 --> 00:42:33.370 So we can observe a fracture or micro-crack under certain 00:42:33.370 --> 00:42:38.160 local stress conditions. We’re just changing from time-step 00:42:38.160 --> 00:42:43.620 to time-step. So once the bond is broken, it does not exist anymore. 00:42:43.620 --> 00:42:51.480 Then the fluid coupling – with solids, it has been also previously developed 00:42:51.480 --> 00:42:57.110 by software developers and now a couple of softwares have it in. 00:42:57.110 --> 00:43:04.550 So here we have system of reservoirs and fluid channels. 00:43:04.550 --> 00:43:10.260 This is a separate numerical scheme that is also communicated in each 00:43:10.260 --> 00:43:17.660 time step with particle DEM model – similar like CFD, but here we can 00:43:17.660 --> 00:43:24.600 flow part of fluid from one micro- reservoir to another micro-reservoir, 00:43:24.600 --> 00:43:29.000 and then the pressure would impose some additional forces 00:43:29.000 --> 00:43:33.840 to our particles, and they would move apart and so on. 00:43:33.840 --> 00:43:37.320 So this seems one-way coupled, and we’re working on 00:43:37.320 --> 00:43:39.890 a two-way coupling, actually. One-way coupled, unfortunately, 00:43:39.890 --> 00:43:46.960 means here that we transfer forces – pressure from fluid into – 00:43:46.960 --> 00:43:51.900 on the particles, so we pressurize the well and then fracture propagates. 00:43:51.900 --> 00:43:56.020 But if we want to squeeze the fluid out of the sponge, this is not in DEM. 00:43:56.020 --> 00:44:01.190 And I thought that it was part of the [inaudible], but actually, just recently, 00:44:01.190 --> 00:44:06.670 some people put it in there. So the full poroelastic seam is 00:44:06.670 --> 00:44:11.430 not yet there, but it’s easy to implement, I think, because we just need to 00:44:11.430 --> 00:44:16.310 put this part of the code in. It will be slow anyways. [chuckles] 00:44:16.310 --> 00:44:18.120 It’s already slow. 00:44:18.120 --> 00:44:25.410 So I tested – this is related now to loading rate. 00:44:25.410 --> 00:44:29.710 So I tested the DEM against different loading rates, 00:44:29.710 --> 00:44:36.720 and I found out that it is actually – response of the model is following 00:44:36.720 --> 00:44:40.980 response of the rock on the – at the low and high loading rate. 00:44:40.980 --> 00:44:47.730 Which I think is great. And this is logical for DEM because, 00:44:47.730 --> 00:44:54.050 in discrete element model, particles – these spheres are kicking each other, 00:44:54.050 --> 00:44:58.260 and then your pressure wave actually propagates in time. 00:44:58.260 --> 00:45:01.580 And time step is very small, so we can observe directly 00:45:01.580 --> 00:45:06.530 the pressure wave and the stress propagation through the model. 00:45:07.860 --> 00:45:11.560 And interestingly, I would say the high – response of 00:45:11.560 --> 00:45:22.020 the high loading rate is also there. So this is not well-understood in physics, 00:45:22.020 --> 00:45:27.620 but it has to do something with the pressure or wave velocity propagation. 00:45:27.620 --> 00:45:32.610 You’re loading the material faster than these pressure waves are 00:45:32.610 --> 00:45:38.280 actually going away from the point where we are loading it. 00:45:38.280 --> 00:45:52.030 So here, for example, now I modeled is two-dimensional cross-section through 00:45:52.030 --> 00:45:57.990 some homogeneous rock – you know, don’t have pre-existing fractures here. 00:45:57.990 --> 00:46:02.790 And I pressurized the wellbore in the middle. 00:46:02.790 --> 00:46:05.900 So time steps are very slow. 00:46:05.900 --> 00:46:13.670 And we can see here effect of the fast- flowing fluid bumping into the wellbore. 00:46:13.670 --> 00:46:18.200 And the damage without fluid infiltration. 00:46:18.200 --> 00:46:26.440 Later, it will be more clear, but here, the blue lines – so red are particles. 00:46:26.440 --> 00:46:30.900 Green are some shear fractures – shear micro-cracks. 00:46:30.900 --> 00:46:34.010 And blue are tensile micro-cracks. 00:46:34.010 --> 00:46:37.870 And this is – the circle denotes pressure. 00:46:37.870 --> 00:46:43.780 So these are micro-cracks. These are all broken bonds between 00:46:43.780 --> 00:46:53.520 particles at higher loading rate, where we have minimal in situ 00:46:53.520 --> 00:46:56.970 compressive stress in the horizontal direction – something 00:46:56.970 --> 00:47:01.540 similar to what is in the reservoir. Maximum in the vertical. 00:47:01.540 --> 00:47:07.330 So for example, here our damage is kind of propagating perpendicular 00:47:07.330 --> 00:47:11.930 to minimum in situ stress, what we would expect from linear elastic fracture 00:47:11.930 --> 00:47:20.190 mechanics. But fluid is not really infiltrating into the fracture. 00:47:20.190 --> 00:47:25.780 So similar thing is happening – not if we – I’m not using here 00:47:25.780 --> 00:47:30.000 high fluid flow rates, but we are using high fluid viscosity. 00:47:30.000 --> 00:47:37.930 Again, in the lab, they got some sort of a darker damage zone and a little bit of 00:47:37.930 --> 00:47:42.650 fracture with high fluid viscosity, and a similar area of micro-cracks 00:47:42.650 --> 00:47:45.810 is what I could observe in my DEM. 00:47:45.810 --> 00:47:50.360 So I will explain in the next slide what I think is going on. 00:47:52.220 --> 00:47:55.340 Okay, so I can see the – here. 00:47:55.350 --> 00:48:03.010 So these are two comparisons, and here is the pressure – 00:48:03.010 --> 00:48:05.030 the wellbore pressure – the same wellbore pressure 00:48:05.030 --> 00:48:09.760 that we are measuring in hydraulic fracturing – and time. 00:48:09.760 --> 00:48:18.050 So we have low-viscosity fluid, first the single fracture can be observed. 00:48:18.050 --> 00:48:21.920 And then these cyan dots are now fluid pressures, 00:48:21.920 --> 00:48:27.440 which indicate that the fluid is entering in the fracture. 00:48:27.440 --> 00:48:32.530 This is with low-viscosity fluid. In low-viscosity fluid, if you look at 00:48:32.530 --> 00:48:40.160 the parallel plate flow formula has the – you know, higher velocity. 00:48:40.160 --> 00:48:44.880 And then we also have some dry deep-fracture dip here. 00:48:44.880 --> 00:48:51.660 But if we – if I’m doing the same thing with high fluid viscosity into the – 00:48:51.660 --> 00:48:54.550 in the wellbore – so we have the same flow rate. 00:48:54.550 --> 00:48:58.180 We are imposing flow rate here and measuring pressure. 00:48:58.180 --> 00:49:03.010 What is happening is, pressure is rising up. 00:49:03.010 --> 00:49:06.300 Fracture is trying to start. 00:49:06.300 --> 00:49:09.700 So I have damage here. 00:49:09.700 --> 00:49:14.880 More micro-cracks, but my fluid is not – does not have time. 00:49:14.880 --> 00:49:19.020 It’s not infiltrating in the fracture because it does have high viscosity, 00:49:19.020 --> 00:49:23.040 and it doesn’t flow so fast. So you know how – if you – 00:49:23.040 --> 00:49:28.071 if you want to use a straw and pull the honey with a straw, or pull the water, 00:49:28.071 --> 00:49:33.070 water is going to come pretty fast, and the honey will really not almost – 00:49:33.070 --> 00:49:37.350 like, wait a little bit and get all red in face. 00:49:37.350 --> 00:49:41.670 So what is happening here, the pressure is building up fast. 00:49:41.670 --> 00:49:43.830 The fluid is not flowing out. 00:49:43.830 --> 00:49:49.850 And then I have the same effect as the high loading – like, the same response 00:49:49.850 --> 00:49:54.270 of rock as high loading – a lot of – like, a lot of damage and fragmentation. 00:49:54.270 --> 00:50:01.310 And here we also observe the drop in pressure, which indicates that the 00:50:01.310 --> 00:50:03.510 pressure would drop here because fluid is infiltrating. 00:50:03.510 --> 00:50:08.770 We are bumping all the time, flowing at a constant rate here. 00:50:08.770 --> 00:50:12.400 But here, pressure is just building up, up, up. 00:50:12.400 --> 00:50:14.820 And fluid is not flowing inside. 00:50:14.830 --> 00:50:22.440 So I – the other thing that I looked at is, this is completely artificial. 00:50:22.440 --> 00:50:30.100 Because I just could change the modulus – bulk modulus of fluid 00:50:30.100 --> 00:50:34.830 compared to rock, which rock could be somehow average – realistic. 00:50:34.830 --> 00:50:46.760 But if I – if I used more stiff fluid, so to say, a fracture did propagate really fast. 00:50:46.760 --> 00:50:53.830 And this is because this pressure – the flow rate is also pressurizing fluid. 00:50:53.830 --> 00:50:59.050 And then the – it’s a question, how is the stress transferred to the tip? 00:50:59.050 --> 00:51:01.920 So how fast is the tip propagating? 00:51:01.920 --> 00:51:09.140 So if we had very stiff, which – of fluid with high modulus, 00:51:09.140 --> 00:51:14.390 which I don’t know what that would be. I even looked online a little bit to 00:51:14.390 --> 00:51:17.840 add some heavy metals into water or something like this. 00:51:17.840 --> 00:51:24.520 So this high – a very stiff fluid would really transfer stresses faster. 00:51:24.520 --> 00:51:31.960 So why I’m talking about this? So here is the fracture velocity 00:51:31.960 --> 00:51:39.670 that increases if fluid is stiffer. So we know – one thing is, 00:51:39.670 --> 00:51:44.250 if we are testing rock in the lab, the fracture propagation, velocity, 00:51:44.250 --> 00:51:48.450 and purely mechanical loading in rock is high – 00:51:48.450 --> 00:51:56.980 like, 2,000 meters per second. Yeah. Like, 80% of Rayleigh wave velocity. 00:51:56.980 --> 00:51:59.470 But then, in hydraulic fracturing, you hear from the field, 00:51:59.470 --> 00:52:04.080 we were fracking for three weeks, and we got 100 meter of a fracture. 00:52:04.080 --> 00:52:07.700 You know, so why didn’t you frack for two seconds, then, if you have 00:52:07.700 --> 00:52:12.720 all those rock? But it’s because there is this coupling is going on. 00:52:12.720 --> 00:52:17.710 And we – actually, you need to transfer loads to the tip of the fracture 00:52:17.710 --> 00:52:22.230 if you want to propagate the fracture. If you want to use fracture mechanics. 00:52:22.230 --> 00:52:31.440 And then this is also the poroelastic effect that is probably taking some – 00:52:31.440 --> 00:52:36.090 having some other effects. I don’t know. Yeah, where is my – 00:52:36.090 --> 00:52:41.100 so this was also very interesting – micromechanic. 00:52:41.100 --> 00:52:46.990 And then the fluid viscosity was low, so the fluid did flow into the fracture. 00:52:46.990 --> 00:52:50.540 And then the third part – also what I did for my Ph.D. 00:52:50.540 --> 00:52:53.660 is to try to see what are the thermal stresses. 00:52:53.660 --> 00:53:01.890 So I found that we can introduce the temperature difference between fluid – 00:53:01.890 --> 00:53:06.270 flowing fluid and those particles and couple the convective 00:53:06.270 --> 00:53:08.690 and conductive heat flow and transfer. 00:53:08.690 --> 00:53:16.220 So conduction is already there in the DEM model, which is based on Fourier 00:53:16.220 --> 00:53:26.630 law, and it’s relatively easy to code it. But this fluid particle part is not there. 00:53:26.630 --> 00:53:36.290 So I used the ready solution for parallel plate flow, and I coupled these – 00:53:36.290 --> 00:53:45.860 I basically looked at – like, a cold fluid going between two hot particles in 00:53:45.860 --> 00:53:50.290 some amount of time, which is my small time-step in the model and 00:53:50.290 --> 00:53:56.160 look at the heat energy exchange and then to see how much is – of the 00:53:56.160 --> 00:54:01.410 energy is extracted from those particles based on mass, and then how much 00:54:01.410 --> 00:54:06.100 energy – how the fluid will heat up. So this is new, and also it was 00:54:06.100 --> 00:54:12.060 published as a new implementation in the DEM model. 00:54:12.060 --> 00:54:14.520 And then, again, I had this conduction 00:54:14.520 --> 00:54:18.350 between particles, so there is no fluid already there. 00:54:18.350 --> 00:54:27.880 So the observation – the general observation, I did just couple of – 00:54:27.880 --> 00:54:33.940 just a little bit of work on that is that, when I compared some nice model 00:54:33.940 --> 00:54:39.870 that I had the fracture propagates under low bumping rate 00:54:39.870 --> 00:54:43.990 and a low-viscosity fluid. And then I used the same model 00:54:43.990 --> 00:54:47.650 to look at what is the effect of temperature difference between 00:54:47.650 --> 00:54:54.500 fluid and rock. If the temperature difference is 150 Celsius. 00:54:54.500 --> 00:54:58.760 So you can see how fracture was shorter. 00:54:58.760 --> 00:55:04.030 It was more branched due to the thermal stresses. 00:55:04.030 --> 00:55:11.630 So I think this would be also interesting in geothermal research 00:55:11.630 --> 00:55:14.520 also looking at acoustic emission – what is going on. 00:55:14.520 --> 00:55:19.260 I think that there must be part of this acoustic emission cloud that 00:55:19.260 --> 00:55:25.660 is related to, just the stresses coming from the temperature difference 00:55:25.660 --> 00:55:30.070 that we don’t understand what it is. And then I don’t even think that 00:55:30.070 --> 00:55:36.580 the big – the large-scale models that are used to predict outcome 00:55:36.580 --> 00:55:39.390 of fracturing have temperature, right, Jack? 00:55:39.390 --> 00:55:46.720 So the thermal effect, I – so this is also a question. 00:55:46.720 --> 00:55:55.710 So there are some other results here where I colored these rock particles 00:55:55.710 --> 00:56:05.200 so you can see how particles are cooling, and then the fluid is infiltrating. 00:56:05.200 --> 00:56:07.960 It’s very small time – computational time because 00:56:07.960 --> 00:56:12.440 of the code is slow on our personal computer. 00:56:13.740 --> 00:56:19.460 We found out the – the major thing that we found out is that, basically, 00:56:19.460 --> 00:56:23.220 the conduction dominates – or, convection dominates conduction. 00:56:23.220 --> 00:56:31.520 That means that conduction will occur in the rock at a very slow rate. 00:56:31.520 --> 00:56:39.300 While wherever we try to – wherever we form new fractures or if the fluid – 00:56:39.310 --> 00:56:44.390 like here, fluid infiltrates into the rock without the fracture around the wellbore. 00:56:44.390 --> 00:56:50.221 We will have instantaneous faster cooling of all the adjacent particles or 00:56:50.221 --> 00:56:56.460 all the adjacent rock. And then, as a consequence, a lot of micro-cracking. 00:56:56.460 --> 00:56:59.510 So these are conclusions. So novel conductive and 00:56:59.510 --> 00:57:03.720 convective heat flow and transport model enables better understanding 00:57:03.720 --> 00:57:07.920 of thermal damage at the wellbore during hydraulic fracturing. 00:57:07.920 --> 00:57:11.160 Fluid, rock, and temperature difference is not independent 00:57:11.160 --> 00:57:15.230 barometer for evaluating the damage. 00:57:16.260 --> 00:57:19.040 Rock permeability, fluid dynamic viscosity, 00:57:19.040 --> 00:57:22.160 fluid flow rate combination plays significant role in transition 00:57:22.160 --> 00:57:25.790 between fracture initiation versus slow cooling 00:57:25.790 --> 00:57:29.410 around the wellbore without any fracturing. 00:57:29.410 --> 00:57:35.461 So thermal stresses are found in this miracle exercises in DEM that they 00:57:35.461 --> 00:57:39.840 cause fracture branching, multiple micro-cracks, fractures the 00:57:39.840 --> 00:57:45.080 wellbore wall, wider fracture zone compared to the isothermal case. 00:57:46.360 --> 00:57:52.000 I have a couple of slides just to share with you some future work. 00:57:52.000 --> 00:57:56.740 So this is the proppant placement that we are working on. 00:57:58.380 --> 00:58:04.580 Also I would like to start new research on liquefaction, piping and dam failure, 00:58:04.580 --> 00:58:10.290 looking at the – using DEM and maybe some experiments. 00:58:10.290 --> 00:58:15.650 The bridge scour and sediment transport. The hydro-thermal-chemo-mechanical 00:58:15.650 --> 00:58:23.350 rock behavior – there is still space to develop this model to make them faster, 00:58:23.350 --> 00:58:28.200 look at the geothermal drilling, fracture propagation, thermal 00:58:28.200 --> 00:58:33.940 mechanical fracturing and rock damage. And then the acoustic emission signals. 00:58:35.140 --> 00:58:39.390 Now I’m also looking a little bit to the sedimentary basins. 00:58:39.390 --> 00:58:50.100 So we found in California that some areas have relatively 00:58:50.100 --> 00:58:57.380 high temperature that are available through abandoned oil and gas wells. 00:58:57.380 --> 00:59:02.720 So I would very much like to see if we can actually retrofit those 00:59:02.720 --> 00:59:08.550 abandoned oil and gas wells for geothermal use rather than drill to couple 00:59:08.550 --> 00:59:16.860 of kilometers’ depth, which would cost, like, 10 or 12 millions of dollars. 00:59:16.860 --> 00:59:22.700 It’s 50% of the cost of the geothermal power plant – the drilling itself. 00:59:22.710 --> 00:59:26.570 So the country is perforated everywhere in the world 00:59:26.570 --> 00:59:29.760 with those abandoned wells. 00:59:29.760 --> 00:59:33.750 And then there is some also classical civil engineering work that I would 00:59:33.750 --> 00:59:39.260 like to work on. So that’s all. Thank you for your attention. 00:59:39.260 --> 00:59:41.640 [Applause ] I hope that I showed you something new. 00:59:41.640 --> 00:59:42.920 [ Applause ] 00:59:42.920 --> 00:59:44.740 - Great. Thanks a lot, Ingrid. 00:59:44.740 --> 00:59:47.740 Well, I think we’ve reached kind of the end of our allotted hour. 00:59:47.750 --> 00:59:49.480 I might encourage you, if you have … - [inaudible] 00:59:49.480 --> 00:59:53.620 - It’s okay. [chuckles] If you have some questions, maybe come up and chat with 00:59:53.620 --> 00:59:57.300 Ingrid afterwards, and we’re going to go grab lunch probably just at the café. 00:59:57.300 --> 01:00:00.730 So you could also join us there. But thank you very much, Ingrid. 01:00:00.730 --> 01:00:03.500 And let’s give Ingrid another hand. - Thanks. 01:00:03.500 --> 01:00:05.540 [ Applause ] 01:00:05.540 --> 01:00:06.960 - Turn that off.