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the fracture which is what you injected for how long and what the pressure is, formation probability and the fracture length. So you want to get the decent, decent I'm talking about. ... Our recommendation always was 30, for, for the, for this value, but ... higher or lower, even if you have lower value it will work well. But you want to make the design, because you lose conductivity with time, for multiple reasons. So you need to have problem that will give you that upper part here, the cond... the probability times fracture with it, so that fracture conductivity. times the fracture width, so that fracture conductivity. You don't change permeability, you change the flow regime inside the reservoir. So, where do you get this information for fracture permeability? Well, you get it from, from, from testing. But you, you know that conductivity will decline with time. There is a closure stress that may crush the problem. You know, this problem will not last forever, especially if you have


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will decline with time. There is a closure stress that may crush the problem. You know, this problem will not last forever, especially if you have cycling. That is very much, that's like when you, you read, when you study metals, you talk about fatigue in metal. So the cycling producing, if you produce, you increase the stress on the problem. If you shut down in production, then the pressure builds up. So you reduce the stress on the problem. So you keep going, the cycling will cause fatigue to reduce conductivity or permeability of that problem. Embedment, part of the, the problem to get embedded into the formation, they are not infinitely stiff, so there is some embedment inside from the problem into the formation, well that obviously will reduce the fracture width and reduces fracture permeability. ... If you don't have the right fluid and the right breaker in the fluid, then there can be gel residues that plugs the, the fracture. Hopefully you work with your service company, or


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and the right breaker in the fluid, then there can be gel residues that plugs the, the fracture. Hopefully you work with your service company, or you avoid problems like that. So this usually not, not an issue. If an issue, then somebody did not do his homework. The fine movement, it can plug a fracture. When people have developed fluid, this is a big, another subject fluids, where you, you, it, it seems counterintuitive, but you, people have added the fluids to propant, is like, it's almost like paint over the, over the propant, so covering a resin coated sand, where it, where it hold the fines, rather than let the fines, the fines move through the fraction. The ... you, you would think it's better for, for the fines to move, the, the only problem when they start moving, they get, they get, they get held near the mouth of the fracture, that's near the wall bore. And that's a disastrous thing to, to happen. ... Another issue is Digenesis. Basically degradation if you ... this is


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that's near the wall bore. And that's a disastrous thing to, to happen. ... Another issue is Digenesis. Basically degradation if you ... this is physical and the chemical degradation. It's ... people that work in welding, they know that when you have two different metals side by welded to one another, you could have problems there. It's like, if you don't treat your battery properly, you end having a lot of junk built on it. With diagenesis is something similar, there is electric current in the form... in all formations, this is the reason you do electric logging. And, and it ... we... experiments have been run and you leave... the experiments have been run and you leave ... leave ... propent in a fracture and water, depending on, on the composition you have there, and you can come back a month later or two months later, it doesn't look like a fracture altogether. There was a very interesting presentations on the subject that I'm not going to get into it. But, but the Digenesis is


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like a fracture altogether. There was a very interesting presentations on the subject that I'm not going to get into it. But, but the Digenesis is very much what ... when you have a limestone ... ... suffering from, from Digenesis and losing it's all permeability. This is the same becoming Dolomite. So that is ... that's a Digenesis issue. So it is, it's a, it is a real issue. So there is, all of that can lead into conductivity degradation most time. So, you look, you will see graphs like this in ... in industry, you get it from... those are published, there is bunch of labs that have done those experiment. You can see, you can see plotting conductivity in millidarcy fluid versus closure stress, and it depends on the problem to concentration, the higher problem to concentration, the, the higher the fracture conductivity. But, as the closure stress increases, the conductivity declines. So, this is function in this, if I using, if I'm using one type of problem. But, also it depends on


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stress increases, the conductivity declines. So, this is function in this, if I using, if I'm using one type of problem. But, also it depends on the size of, of that problem. So, so there is multiple, multiple cases. So the first case we talked about, about the concentration, here I'm talking about the size, here is 12x20 mesh, that is the biggest one, ... this is the... 2040 is the one, most sandstone formation 2040 is, probably the one that's most commonly used. ... Sometimes if the formation is fairly high probability, you may fill in with, with bigger problem. To keep, to make sure that the fraction is open at the mouth of the fraction, you know what. It also depends on the type of problem. ... We hear when I use Ottawa sand, and when you talk about sand, just when I attract your attention, it's not sand you find on the beach, or find in the Sahara. Those are, are sands that are mined. So they have not been exposed to, to atmosphere for millions of years. So they are all sand


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find in the Sahara. Those are, are sands that are mined. So they have not been exposed to, to atmosphere for millions of years. So they are all sand that's exposed to atmosphere for many millions of years, they are cracked and they are very weak. So they... and they are not spherical, So they, they have a bunch of issues. So when you get talk about sand, natural sand is being used, is usually, it's always actually, not just usually, it's always mine the sand. You, you mine them from underground, and then you see if they spread them into different sizes and so on and so forth. But there is also man-made material, Bauxite for example. Bauxite is Aluminum Oxide, you, you can have, it's a lot stronger. So if you have very deep well, if you have shallow well, you may use natural sand, it's cheaper to use. As the formation gets deeper and deeper, then you need to use stronger and stronger propent, otherwise it will... otherwise it will crush. There is some formation in the Gulf of Mexico,


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then you need to use stronger and stronger propent, otherwise it will... otherwise it will crush. There is some formation in the Gulf of Mexico, that is... of Mexico that is, that almost 6 miles deep, was a poor pressure of 20 plus thousand PSI. So that's extremely high. So you have to, to fracture it and those are, I've been, I was involved in some, when we designed some fractions for them, were ... uses a very special prop and, and require a special procedures to, to work with. So, as the formation gets deeper, higher pressure, you wanna use ... better, stronger problem, maybe bigger problem. better, stronger problem, maybe bigger problem. So, this kind of schematic telling you what kind of, depending on the closure stress, what kind of problem you would use. So, very much a summary of what I said, is lower stress, you may wanna use sand, as the stress gets higher and higher, you wanna use a stronger and stronger Proven. There is actually Proven right now, I'm not going to mention


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as the stress gets higher and higher, you wanna use a stronger and stronger Proven. There is actually Proven right now, I'm not going to mention the name, it's commercial products, but they try to produce Proven that is more spherical and one size, so instead of saying 20, 40, it says only 40, so it is uniform size. The uniform size will give you a higher conductivity and also give you a higher strength. There is a very, very good paper, interesting paper by this gentleman, Terry Palash, SPE number is given here, interesting paper by this gentleman, Terry Pellish, SBE number is given here. I asked him to provide me some slides. So he sent me all the slides. I'm just going to use a few of his slides there. I, if you want to get more into profit, I suggest that you read his paper. Really, really excellent paper. ... He's talk about the crushing test, because in order to get this conductivity, you need to run a special test. So, he ran, he went through all those testing, he was for


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crushing test, because in order to get this conductivity, you need to run a special test. So, he ran, he went through all those testing, he was for Carbocer ceramic, at least he used to. And he said, usually those are the assumptions that the crush test simulate realistic condition, everything is reliable and repeatable, the weight is, does not affect ... crushing, experiments, uniform packing, and he has lies to show that, none of that is really true. So, you have to be careful in picking up. So he ran, ran experiments ... and found out that, first that's the procedure they do, they, it is the equipment they, they used. ... And it said we'll, we'll, we'll ... work with it before and after. They found out it's, are the results repeatable? Not really, you can see in cases here, is a big difference in the results repeatable? Not really, you can see in cases here, there's a big difference in the results. Some are good, some are good, the difference is very small, but there is some that


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can see in cases here, there's a big difference in the results. Some are good, some are good, the difference is very small, but there is some that are, from one test to another, here you see test one, two, and three, from one, two, and three, there is a, is a big difference, it can be up to 50% change, so. So, sometimes you have to take this with a grain of salt. I think pinch out can, can be an issue, pinch out can be an issue. Provence pillars, although sometimes we're going to see we people may design for Provence pillars. So you don't really have as uniform packing arrangement inside the fracture as we think we do. This one reason when you analyze data, it may not behave or did not give you exactly the results you think you achieved. There is other designs. Now many people instead of at least a few years ago or started looking at, hey, instead of, instead of trying to get uniform packing in the fraction, maybe doing something a little different. One of them like partial monolayer.


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instead of, instead of trying to get uniform packing in the fraction, maybe doing something a little different. One of them like partial monolayer. Partial monolayer meaning that I have sand and in between, one layer of sand in between, there is nothing, nothing at all. It's just the fracture is open. If you remember the equation that I showed you last week and the fluid flow part, I'm showing you equation of fracture that is open. The permeability of an open crack is basically infinite. It's extremely high permeability. open crack is basically infinite, is extremely high permeability. So that's the idea behind partial monolayer, saying that if I have a propant that is keeping areas in between extremely high, so the average is going to be very high permeability. Well, yes, that is true, but this works only when you, when you have, when you don't have very high stress. ... Because, if the distance is very large, the fracture will pinch out in between. You, you end up having no, no


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you don't have very high stress. ... Because, if the distance is very large, the fracture will pinch out in between. You, you end up having no, no conductivity whatsoever, no permeability. So there is, so the, you, you apply those techniques with, with, you know, it's, it's not just one solution fits all. ... Pillar frack and the highway frack, they are, and conductor frack, they are all the same thing, and that is ... this, with, with names given by different, ... different service companies. And basically saying, a pillar frac is a very old idea, is similar to partial monolayer, except you say, well I do have multiple, multiple layers inside the fracture and in between, so I have a pillar and pillars and between the pillars I have basically empty area, so open fracture, so the average is, is very high probability. And it actually, you know, I've seen results in more than one country, in one place, and you can't argue with success. They do work well. The production was a lot higher,


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know, I've seen results in more than one country, in one place, and you can't argue with success. They do work well. The production was a lot higher, at least initial production. The one thing one has to worry about is to look at the long-term production. So make sure that you don't have sharp degradation or closure pinch out inside the fracture. This is one case that I have seen. This company run this case in Eagle Ford and said, hey, they did it using one of those fractures, I think it was a conductor frack, and it saved the 1 million pounds of profit. But the one thing one has to remember here is also this is an Eagle Ford. And so the production from natural fracture is very important, and the formation has, itself has very low probability. So you do not need really a huge amount of, of problems. When this was the conductor frack, where you have 30 second burst, so your, your system is, the injection is set to half burst every 30 seconds of problem. It ... it did, at least the


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where you have 30 second burst, so your, your system is, the injection is set to half burst every 30 seconds of problem. It ... it did, at least the claim that it did work, it produced at least as much fluid when saving is one million pounds of sand. Fraction fluids, you wanna get it, your... fraction fluids will give you viscosity that controls weight, that impact the transport. You have control fluid loss, so you... you... you build a filter cake, very much like the mud cake that you... you see in drilling. In drilling you... you wanna build the mud cake to prevent drilling fluid to leak into the formation. Here you do similar thing, you filter cake, so it is a similar concept. So you lose a little bit of fluid and it builds a filter cake, so you, it prevents further loss. ... It has, it provides some density, and it gives you a hydrostatic head. And also it helps in, in settling of the fluid, both the viscosity and the density will help in ... in settling, control settling of


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head. And also it helps in, in settling of the fluid, both the viscosity and the density will help in ... in settling, control settling of Profit. ... Friction pressure, it, you wanna reduce friction pressure, otherwise this is, this would be horsepower that you would ... one would be losing. And, you wanna control cross linkers, you wanna make sure you don't damage the formation, this will get into... into it in a minute. Fluids, when you look at fluids, I'm sure that you, all of you, know about that. I have Newtonian fluid, basically if I plot shear stress versus shear rate, if I have Newtonian fluid like water, then it's a straight line, basically at zero shear stress, I have zero shear rate, there is no movement, and it is, follows linear behavior like this. The slope of this line is your viscosity of the fluid. Okay? In... in all industry, in fracturing, you are not using Newtonian fluid, you are using non-Newtonian fluid. Non-Newtonian fluids, it can be different types. One is


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in fracturing, you are not using Newtonian fluid, you are using non-Newtonian fluid. Non-Newtonian fluids, it can be different types. One is Bingham plastic, which it takes yield stress. So, there has to be some stress before the fluid can move. And this is important to make sure that, that ... cuttings do not drop to the bottom of the well, when you stop circulating, otherwise it becomes a huge issue. And then from there, it can either follow up, the fluid follows a straight line, it'll be like Newtonian fluid, or it could be actually even a curve. For the non-Newtonian fluid that we use in fracturing is the pseudo-plastic, so it is, it's a curve like this, where we say, shear stress is equal to some constant, times shear rate, raised to some power. We'll write the equation in a minute. So it is a, is a equation of a curve where that power which you're in the prime is less than one. So let me show you the, the equation, here, this is the power law, power law equation. It's this


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power which you're in the prime is less than one. So let me show you the, the equation, here, this is the power law, power law equation. It's this constant, K' times, Shear rate, times to the power of N' and N' is less than one, so, so here, so what is the viscosity of this fluid? Well actually, there is no viscosity, there is an apparent viscosity. So, you, you can see, as it gets, I'm going to talk, I'll show you a question for apparent viscosity, but the apparent viscosity here, is basically, if I wanna get the apparent viscosity at this point, I draw a straight line down to zero. So you can see that the straight line gets flatter, and the flatter as the shear rate gets higher. So that is shear thinning fluid. So it acts as a, thinning fluid. So it acts as a, as a lower viscosity fluid as the shear rate gets faster. So that's what you use in fracturing fluid. And this is opposite to dilatant, that you do not use dilatant in fracturing fluid. And dilatant is the exponent, the


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you use in fracturing fluid. And this is opposite to dilatant, that you do not use dilatant in fracturing fluid. And dilatant is the exponent, the exponent is larger than one. And so you can see that the shear rate, as the shear rate gets larger, the apparent viscosity gets higher. And so here is what I, basically this is the equation for the model and apparent viscosity here, you can see for fracturing fluid, the apparent viscosity is the slope of this line. So as the shear rate gets larger, the fluid behaves as if it is thinner. So it's a shear thinning fluid. And the equation for apparent viscosity looks like this. Many people think it is the tangent. So please make sure you understand that it is the line going from zero to that point. And so, if I have a linear gel, water, the N prime is one. This is the K prime is 1, this is the K prime, is that value, the viscosity as you put it in, in, in this little, you apply the shear rate to it, at shear rate of 170 inverse of a second,


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K prime, is that value, the viscosity as you put it in, in, in this little, you apply the shear rate to it, at shear rate of 170 inverse of a second, you, water is 1, basically the viscosity is constant, it's 1. Linear gel, linear gel is, NA prime is 0.8, if you have cross-linked gel, we're not going to get very much into that, the NA prime can be as low as 0.5. So, the requirement, I'm... we're running out of time, so I will just show you those... It has a lot of requirements, one of them is to maintain... it has to be cost effective of course, but you wanna maintain viscosity. You wanna maintain viscosity, you to have the fluid to keep the propant being held in place, until you try to close that fracture. And you want to be able to, to adjust this viscosity. You see this is, I will let you read this requirement. ... There is water based, like what we discussed before, most of the fraction fluid now is water based. At one time people used a lot of energized fluid, ... Nitrogen, CO2


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like what we discussed before, most of the fraction fluid now is water based. At one time people used a lot of energized fluid, ... Nitrogen, CO2 or a mix of the two. This is the foam based fluid, it's not used as much, in the presentation I'm going to send you, I was going to tell you why, essentially although foam is very good in carrying propant and transporting prop, foam does not have much Hydroceticate, so... So, it has a special application. Oil based fluid, is ... it's still being used, but is not as... as popular, because of ... potential risk factor. ... The people have used the Acid, we use the Acid a lot in ... in fracturing Carbonate fluids. ... Oh yeah. Not going to get much in, so linear gel, there is different kinds. This I will, I will leave it up to you to, much in. So, linear gel, there is different kinds. This I will, I will leave it up to you to, to read, especially chemical names like this is, is not that easy to pronounce. But, we have used Acid, Acid Frags and


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I will leave it up to you to, to read, especially chemical names like this is, is not that easy to pronounce. But, we have used Acid, Acid Frags and Acidizing in general. We actually spend, acidizing in general. We actually spend ... in, in the regular class, we spend some time on, on acidizing. Because it can be very important, especially in Carbonate formation. There is even Acid has been used for sandstone, you could acidize sandstone formation. However, when you acidize sandstone formation, is essentially to remove damage. For Carbonate formation is to, is to create wormholes or improve average permeability around, around the workbore. ... Cross-linked fluid ... you, you wanna use it when, when you have high problem concentration. If you're fracturing shale, you probably do not need to do that, because you do not need to, to use much, much problem to concentration at all. And, cross-linked fluid can be different types with. Some of these heavy metals are being frowned upon right


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much problem to concentration at all. And, cross-linked fluid can be different types with. Some of these heavy metals are being frowned upon right now. People don't want to use ... Titanium, Zirconium or, or even Aluminum. ... You, now there's a lot of move towards using organic crosslinkers. We, I know we, we got involved very much into using organic crosslinkers for, for, for conformance fluid, and same thing applies to, to fraction fluids. ... So, the crosslinkers depending on, on what you use, ... Titanium of course is, it is permanent, it's shear sensitive, it, it can be variable. There is, there's a lot of decline in using things like that. ... Because, they, they are cross, they are cancer causing agents, and many, many places actually prevents you from, or prevents service companies from using heavy metals and, and fluids. Energized fluids, we talked about it already a little bit. Energized fluids, we talked about it already a little bit. It's... it was more popular in... in


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fluids, we talked about it already a little bit. Energized fluids, we talked about it already a little bit. It's... it was more popular in... in 80's and late 80's, basically for... for reasons for carrying propent and if it's not very deep formation. There is very low leak off, so it is ... it works very well in this situation. And so, and so here basically is loss control, is carrying ability, but ... the biggest disadvantage is lower hydrostatic head, and it may have very high friction pressure. In models, we'll, now I have, people, we used to use, we used the 2D model years ago, people now do not use 2D, we use 3D and the full 3D models. You can look at it, 2D models is, people have stopped using it for a very long time. It's basically because of computers now are a lot more sophisticated, you can run models very fast, both the pseudo 3D and the full 3D models. The full 3D models have the advantage of looking at layering system in a more complete way. So that's actually what you


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3D and the full 3D models. The full 3D models have the advantage of looking at layering system in a more complete way. So that's actually what you want to use is the fully 3D model. It gives you maybe a better picture of what is going on. So the 3D model, although it may look at the stresses, but does not look at the layering system and what is going on really accurately. And very similar to the fluid flow models. You wanna have fluid flow models, you want to look at 3D model, looking at what is going on, the effect of each layer accurately, rather than, rather than approximating that behavior. So lately we, everybody has been working on the fully 3D model. Starting the mid 90s, the use of 3D model has mushroomed. Even at University of Houston, we're developing models, where we develop the full 3D model. Because when I look at stresses more accurately, when I look at layers more accurately, you wanna see these effects and design your fractional treatment. ... So, a 2D models is not


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more accurately, when I look at layers more accurately, you wanna see these effects and design your fractional treatment. ... So, a 2D models is not being used, I need to remove it from here. Pseudo-3D model, there's two different types, some are really used cell model, but the ones that you really wanna be using, is, is fully 3D model model to calculate height, width and length correctly. A pseudo 3D model there's a lot of assumptions where you really don't, don't calculate the tree, although they pretend to be calculating all those models but, but it's with a, with a great deal of assumptions. So that takes care of the presentation. I'm going to put in, I put it in Researchgate and I'll send the link to Dr. Elgarhi where you can download this presentation. What I'm going to put on is going to be a little bit more expanded presentation. Thank you, Dr. Solomon for a very informative webinar. I'm sure the audience has benefited greatly from it. In the meantime, I've collected a few


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Thank you, Dr. Solomon for a very informative webinar. I'm sure the audience has benefited greatly from it. In the meantime, I've collected a few questions for a quick Q&A session. What are the reservoir quick Q&A session. What are the reservoir parameters we can get from the square root of time technique and the g function? Okay, I'm going to cover the g function next week. So I, g function does not give you reservoir properties. It actually gives you leak off coefficient. There have been techniques that were developed to analyze the data, the same data to get formation probability. I will go through those techniques. We have, we developed our own techniques as well as those techniques and, and literature will cover all of those next week. So maybe we need to wait for next week to talk about. G-function is very important and we'll cover it. There's some advantage, disadvantage of using G-Function, but we'll discuss it next week. So that will be an incentive for you to attend the next


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it. There's some advantage, disadvantage of using G-Function, but we'll discuss it next week. So that will be an incentive for you to attend the next week. The second question is, how can we solve an issue of propane flow back near wellbore? That's a very good question. And I have seen this issue many, many times. We actually working on, we have a PhD dissertation, the student that's working on an issue like that. We have, there was always suggestion that you tail end with maybe resin coated sand. One thing is not to follow the treatment with water thing is not to follow the treatment with water or with non-carrying fluid. So when you have problems moving into the whirlpool, you're being replaced by problem to deeper. but having resin coated sand or some treated propent is, is probably the best, the best idea. ... You could allow for fluid to leak off for short time before you, you start flowing back, because the... just I need to mention, you, you wanna do some flow back to close the


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to leak off for short time before you, you start flowing back, because the... just I need to mention, you, you wanna do some flow back to close the fracture, because you don't wanna wait for forever. So, if you have resin coated propent, that may or similar, there is multiple, multiple types of fluid, there's some use fibers for example, that's another commercial techniques to show you. That, that will allow the problem to be sticky near the, if you, if you follow a futility with, with this type of problem, it becomes a sticky near the wheel bore, so it prevents it, allows only fluid to move in without having the problem moving back. But that's always an ... a big issue. ... Another question is, which size of propent is commonly used with shale fracturing? They ... most of the propent I've seen was essentially sand. ... You know, I know that various types of sand, like Brady sand, well which is not being used anymore, but ... So, you do not need huge conductivity in shale. ... The


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that various types of sand, like Brady sand, well which is not being used anymore, but ... So, you do not need huge conductivity in shale. ... The reason for that is for, if you look at that equation, formation permeability is very, very small. And so you, you do not need very high fracture conductivity. Sometimes your people would tell you that the mere fact that you open up the fracture, the... the... just... just the... the grains from the formation will give that fracture high enough conductivity. I always recommended that you use some prop... So people... I think, I believe sand is ... is the most common ... proper to use in there. But that's a good question, I will, I will... Things keep changing, I will double check on it and I will let you know next time. But I... the cases I've been involved in was mostly sand. For... I'm talking about for shale. Another question, Dr. Solomon, you mentioned KIC and HS. What is the relation between them? Between KIC and what? HS. HS? Yes. What


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about for shale. Another question, Dr. Solomon, you mentioned KIC and HS. What is the relation between them? Between KIC and what? HS. HS? Yes. What is SHS? H S? Yes. What... What is S H S? I'm not sure the question is... Maybe he means a horizontal stresses for example? I ... I don't know what he, this, when he stress you say sigma. We talked about later on and. Dr. Solomon, you know, because he is writing and he cannot have the Greek. Oh, I saw. Maybe he mean horizontal. No, no, no, no, no. Okay, this one. Yeah, I, now I, it's talk about height. Okay, this is formation thickness. H is formation thickness. HS is the penetration of the fractures into the upper and lower zone. So, if I have symmetric case, I'm calling this HS. This is ... actually I ended the calling it A and B in the next equation. This KIC is a property of the rock, not of the fracture. It's a property of the rock. When we look at it in sandstone, we say KIC is 1200 to 1500 P size per root of inch. That's property of


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of the fracture. It's a property of the rock. When we look at it in sandstone, we say KIC is 1200 to 1500 P size per root of inch. That's property of the rock. That is the value that the fracture has to overcome and in order for it to propagate. So in this case, the stress intensity factor, not the critical factor, it will be the pressure inside the fracture, P times this whole thing, which will be H over two plus HS. Okay? So if this value, the pressure times that height is higher than KIC, the fracture will continue to propagate in height. So it is the height of the fracture at very early on before it propagates into the upper and lower zone. If the fracture is so small here, then you're talking about, you're talking about the pressure times that height. Okay. Did I answer your question? So. I think you did Dr. Solomon. Yeah, this concludes our Q&A session. There's another question about G, about the square root of time and g-function, but we'll save that for next webinar. Yeah,


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our Q&A session. There's another question about G, about the square root of time and g-function, but we'll save that for next webinar. Yeah, we'll cover the analysis next time. I may expand it. Testing, you know, it can take a lot of time. We'll cover some of it and then we'll see. Yeah, so yeah, thank you Dr. Salomon for deciding some of the time of your surely busy schedule to give this webinar. We are all grateful. Thank you attendees for tuning in from all over the world. Stay safe, wear a mask and have a great day. Thank you very much. Stay safe, wear a mask, and have a great day. Thank you very much.


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So good morning, good afternoon and good evening. Hope you are all doing well and staying safe. I am Maryam Shref, a senior petroleum engineering student at the Lebanese American University, and I'll be moderating today's session. So it's my pleasure on the behalf of Payo Petro to welcome you all to the fourth and last lecture of the online course, Hydraulic Fracturing, which has been presented by a special distinguished speaker, Dr Mohammed Solomon. I'm sure that his participation with us has benefited all attendees and added a lot to their knowledge. So let me begin by reintroducing Professor Solomon. So Professor Solomon is the chairman of the Petroleum Engineering Department at University of Houston. Dr. Solomon has a long industrial and academic experience. He holds 35 patents on fracturing operations and analysis, testing and conformance applications. He is the author and co-author of over 250 technical papers and articles in various areas of petroleum engineeringventors. He is


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applications. He is the author and co-author of over 250 technical papers and articles in various areas of petroleum engineeringventors. He is a professor of political papers and articles in various areas of petroleum engineering. Dr Solomon is a registered professional engineer in the state of Texas. He is also a distinguished member of the Society of Petroleum Engineers and fellow of the National Academy of the Inventors. To highlight he authored several books book chapters on stimulation and testing. Additionally, he's the primary editor of Fracturing Horizontal Wells, published by McCrowhill in 2016. He's the author of Optimization of Hydraulic Fracture Stages and Sequences in Unconventional Formations, published in 2018 by CRC. Finally, Dr. Solomon holds a Bachelor of Science with top honors from Cairo University and the PhD degree from the University of California, California, PRC. Finally Dr Solomon holds a bachelor of science with top honors from Carter University and masters


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from the University of California, California, PRC. Finally Dr Solomon holds a bachelor of science with top honors from Carter University and masters and a PhD degree from Stanford University, all in petroleum engineering. So please join me in welcoming Dr Solomon. So, Doctor, we are pleasured to have you with us today and thank you for the time you have dedicated to deliver this course and for supporting a bio Petra's vision and mission, which is mainly focused on maximizing oil and gas digital content and raising educational standards by providing students, professionals and members with a large library of digital resources. And on a final note before proceeding with the session, if you have any questions related to the technical content of the presentation, please feel free to drop it down in the Q&A section, and we will try to answer as many questions as possible. And as a reminder, don't forget to solve the last quiz for this course and do the final exam, which will be held on


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as many questions as possible. And as a reminder, don't forget to solve the last quiz for this course and do the final exam, which will be held on Tuesday, the 3rd of November, at 2pm and 8pm Egypt time, and also 2am Egypt time Wednesday. However, you are only allowed to attend and submit one exam, depending on the time and date that suits you the most. Without any delay, Dr. Salaman, the mic is yours. Thank you very much for the introduction. Good morning everyone or good evening, depending on where you are. It is 10 in the morning here in Houston. This is the last lecture we're going to discuss on fracturing testing. Please remember this is an introduction to fracturing, it's a very basic school. Testing or any of the subjects we have discussed so far would take many hours to go in in details on them and that is definitely for in details on them. And that is definitely for testing too. I will introduce you to testing, which is specialized to fracturing. Parts of it, in order to go


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on them. And that is definitely for testing too. I will introduce you to testing, which is specialized to fracturing. Parts of it, in order to go into all details, one has to have, a student has to have a background in wood testing because some is built on wood testing as well as on fracturing issues. So let us, let us start talking about it, let me see. Why tests are runs? Well, tests are runs like in what we see in well testing. We want to understand the formation, however tests and fracturing, they are run to get not just the physical properties but mechanical properties as well. If you are familiar with this thing, you run it, you say I want to get formation probability and skin factor. Here you may want to get also mechanical properties or stress field. When we discussed ... fracturing in the last three lectures, we talked about the importance of mechanical properties, we also talked about the stress field, the magnitude of stress, as well as the orientation of stress. So, some


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importance of mechanical properties, we also talked about the stress field, the magnitude of stress, as well as the orientation of stress. So, some of those tests are designed to get those properties, because they affect the fracturing very much. So it goes beyond the, just the physical properties. So there are techniques where you calculate formation probability, or initially you calculate a leak off coefficient, you wanna calculate fraction length, fraction efficiency, we'll talk about all of that. There are newer techniques that have been developed and being developed, not just ... So, we'll mention some of those techniques, we are not going to discuss them in details, there was a lot of research including including here at the, at University of Houston, I have several students working on different areas that you find very interesting, including a paper that we, one of my students just presented yesterday in the annual technical conference. And once you get all this information,


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including a paper that we, one of my students just presented yesterday in the annual technical conference. And once you get all this information, you're going to predict the formation response, response during the fracturing process, you're going to predict the production, what happens, you're going to optimize, you're going to get the best fracturing treatment, and optimum fracturing treatment. The type of tests, we are going to talk about several types. Some of them, I'm going to call them pump and flow back tests, we'll talk about the step rate test, step up as well as the step down tests. They are a little different, it's not exactly the same thing as we are going to see in a minute. And we are going to talk about pump and shutting tests. You call it DFIT, you call it Manifrac, depending on. DFIT is the name that's used mostly now, although you are going to find the name Manifrac used a lot at one time. People called it also DataFrac, Data data test, FAT, but most of the time now


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you are going to find the name Manifrac used a lot at one time. People called it also DataFrac, Data data test, FAT, but most of the time now people refer to it as DFIT or mini-frag. Then you have leak of test and extended leak of test, that's during drilling and when you think about it, it is really not very different from what we have in DFIT except it's during drilling. We analyze the sum of this data very much like what we, the way we analyze DFIT. So it may be only name and the, the, when you run the test. So let us talk about, first about pump and flow back test. And that is type of test which we used to, we have run many, many years ago, but maybe in late eighties, early nineties, was very popular. We called it a micro frac. And as you are going to see in a minute after we discuss it, it actually is making a comeback and many companies are rerunning this test but not exactly the same way we used to do it in a little different fashion, I would say. In this specific test, it was,


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are rerunning this test but not exactly the same way we used to do it in a little different fashion, I would say. In this specific test, it was, the idea was to create a small fracture, fairly small fracture, and ... the, the reason you wanna create small fracture with smaller ... injection volume is, is to make sure that the stresses inside the formation don't change very much. So that is the reason behind it. And we're looking, we're going to look at the test in a second. Once you, you fracture the formation, and you are doing it during drilling. So I go into the area where I, even above the pay zone, above the pay zone, in the pay zone, below the pay zone, above the pay zone, in the pay zone, below the pay zone, create fractures there, and ... if I analyze the data, the pumping and the flow back, I'll be able to get when the fracture closes, and I say, hey, when the fracture closes, this is my minimum in-situ stress. The reason is very close to minimum in-situ stress is because the


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and I say, hey, when the fracture closes, this is my minimum in-situ stress. The reason is very close to minimum in-situ stress is because the injected volume is very small. Once I do that, I recover an oriented core. And that oriented core can tell me a fracture orientation. We'll look at the examples in a minute. So I can determine closure pressure, which would be essentially the minimum situ stress. I will recover a fracture and that will give me the orientation. So I, from there I determine the stress field, the magnitude and so. So, so what, what we, we, the idea behind this test is to come down to the area where I want to test, and this is during drilling, and this can be, as I said, above the pay zone, in the pay zone, below the pay zone. Actually, the recommendation was to do it in the three areas, to get stresses in the pay zone, as well as in surrounding zones. Like what we discussed last time, to see whether fracture would propagate upward or downward. So I put the drill


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as well as in surrounding zones. Like what we discussed last time, to see whether fracture would propagate upward or downward. So I put the drill pipe and I replace the drilling bit with the perforated anchor, like what I see here, I put an inflatable packer, and we go down, we isolate... we... we isolate this area at... at the bottom here, or the bottom of the well. I received the packer, inflate the packer, so receive this area, so it will be isolated. I inject inside the drill pipe. I fracture this formation, and the fracture as you can see, is going to go sideways, it going to go upward also, and monitoring pressure both below, below the packer, as well as inside the drill pipe and in the annulus. Once ... I can tell right away whether, whether the, the fracture whether the fracture got around the inflatable packer or not by monitoring the pressure. So usually what we did, if I see a higher pressure in the analysts, I would stop the test, because obviously the fracture went above


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the pressure. So usually what we did, if I see a higher pressure in the analysts, I would stop the test, because obviously the fracture went above the package. So we could, once you've done the test, I pull out the drill pipe, I go back with a coring tool and I core an oriented core. Oriented core, basically I'm going to see one in a second. It is a core where it is etched on the side, and the service company would tell you, the coring company will tell you which orientation that line is, it's like a scribe mark on the core. So, if I know it is, it, it tells me this line here is in, in say, 20 degrees East of North, ... and the fracture is going 70 degrees ... to it, then I know exactly the orientation of the fracture in space. So, that is the, the whole idea. ... This, I showed you this test before, that was actually a micro-frag that was run, you can see the breakdown pressure, we shut down, then we inject it again, we reopen pressure like what we discussed before. And I find that


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was run, you can see the breakdown pressure, we shut down, then we inject it again, we reopen pressure like what we discussed before. And I find that fracture closure pressure that I find here, and we'll look at more detailed tests in a second, that since I injected very small amount of fluid and you'll be surprised, we used to inject just a couple of barrels over a few minutes. Since the volume that was injected was very small, the fracture, the stresses inside the formation have not changed. So my closure pressure would be very, very close to my minimum in-situ stress. So as, as the injection pressures, injection volume gets a higher and the higher that fluid will leak off and the value that I see in closure pressure may become different from minimum in-situ stress. So let's just look at an actual case that this part of a paper that we published some time ago myself and Dr. Ali Danesheh in SPE21400. This is some time ago when we ran this microfrag and you can see we're injecting


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we published some time ago myself and Dr. Ali Danesheh in SPE21400. This is some time ago when we ran this microfrag and you can see we're injecting here at about eight gallons per minute. It lasted about 15 minutes or so from 10 to seven, to seven, five to seven to 10 minutes after seven. So for 15 minutes, eight gallons, that's 120 gallons, that's a little less than three barrels of liquid. So you inject and right away, we will flow back. And I'm flowing back here at about three gallons per minute. This actually required developing or building a special tool to be able to control that constant injection rate. It's a lot easier in situations like this to inject at a constant rate than flow back at a constant rate. So always flow back at constant rate is fairly difficult. And we want it to flow back at a rate that will give us the pressure drop. You see here, I'm fracturing and fracture propagating for only 15 minutes, I'm shutting down and I want to get an inflection. At least this


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drop. You see here, I'm fracturing and fracture propagating for only 15 minutes, I'm shutting down and I want to get an inflection. At least this was the idea we had at the time, that if we see the inflection, and people used to argue, what the closure pressure? If you read that paper, we did complete analysis, not only on this test, this was one example, but in multiple tests like this, and we figured out, at least we were at the time, and now we believe that this would be, the area here would be the full closure at a little less than 6,400, that dashed line. So that would give us the closure pressure and minimum situ stress. Look at this, some of the cores that we recovered. I hope you can see this line here. You see, you can see the fracture where it broke, where the recovered this fractured core. But above the fracture at an angle to it, there is a scribe mark. And this is like etching in... in the core. That is your... that is where I said, the coring company will come and tell


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it, there is a scribe mark. And this is like etching in... in the core. That is your... that is where I said, the coring company will come and tell you that, Hey you, your fracture or your... your core was oriented at such and such ... degree. So you... this was a vertical well, is not a deviated well. And so I look at it, I know the orientation of... of the core, I know what angle is the... the fracture is located with respect to the core, then I... I know exactly orientation of, of the stress. Because I know that the fracture is perpendicular to minimum stress, I know the orientation of the fracture, I know the stresses, I know the orientation of stress, and the test also give me the magnitude of stress, so having these two together works very well. So, that defines the stress field. This is another example, the long example, where we recover the longer core. This was also interesting because, if you look at the corner here, and you can see this is the end of the fracture. So it ...


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the longer core. This was also interesting because, if you look at the corner here, and you can see this is the end of the fracture. So it ... it shows how the fracture ended. Actually it went to an angle to, to the core. And that is ... several feet of ... of core. It's probably about 5, 6 feet or so. And that we brought to, this we brought it to our lab. This is something that we did myself, and we're taking those pictures. Can you run it on wire line tools? Absolutely. Actually, even at the time we, those ideas of running on wire line tools and many companies right now, they have come up with better equipment to be able to run that micro frack after you drill the well. So you can run it on the various tools. I know that Slumber J built a more advanced MDT that is still selling very well. But other companies, I'm sure they are doing the same thing. RDT, I think with Halliburton, CRD with Baker Hughes at the time, whether they maintain them or not, I know MDT and RDT is still used


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the same thing. RDT, I think with Halliburton, CRD with Baker Hughes at the time, whether they maintain them or not, I know MDT and RDT is still used very much and they are running them in microfrag. ... Some people, it's almost funny, but they did not realize that we have been running microfrag on drill pipe, many, for a very long time, and we did it first as research, then as a, as a service. ... However, the way we, when we ran it on drill pipe, we extracted core, you know, we recovered an oriented core. Of course, after you drill the well, there is no more core zone, you're running a wireline tool, formation tester. So, no core is extracted. So, you can determine formation, you, you will be able to say something about stresses, you could even before that, you can run a well test and determine formation permeability. The step rate test, step up, sorry for this, not sure what it is, but for a step up, step up rate, basically you are stepping up the rate from below fracturing to


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test, step up, sorry for this, not sure what it is, but for a step up, step up rate, basically you are stepping up the rate from below fracturing to above fracturing, and the idea is to determine the fracture opening pressure. So this is a real example we have run, I was a co-author on that paper by Stanton. We went to the field and we ran bunch of tests. One of them was a step-up rate test. Basically, you're starting at low rate, you monitor the rate for ... you keep constant rate for a little bit of time, monitor pressure, then increase the rate, monitor pressure and so on. And, it, it would look something like what we have here, and then... the, the idea that before the fracture is opened, the, you, to increase rate from one value to another, it require fairly high pressure, high pressure increase. So that the interval in the stem pressure is high when the formation is not fractured. Once you fracture it, then it is easier to inject the fluid. So you go from one rate to a little


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is high when the formation is not fractured. Once you fracture it, then it is easier to inject the fluid. So you go from one rate to a little higher rate, you don't have to increase the pressure as much as if it was not fractured. So that is the basic idea. That has been done many, many times. And it looks something like that. This is very much what I'm saying. So I plot bottom hole pressure versus injection rate. And you can see before fracturing, in order to, the gradient is high, which tells me for per unit pressure increase I need, per unit rate increase I need higher pressure. So that gives me a higher slope. Once the formation is fractured, it should be lower slope. I can increase the rate without increasing the pressure very much. So if I have data below and above fraction opening pressure, it will look something like this. I will draw two straight lines. The intersection of the straight line is my extension pressure. And so it is, this test has been done many times. It's very


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draw two straight lines. The intersection of the straight line is my extension pressure. And so it is, this test has been done many times. It's very valuable test to do. The even better test that was developed several years ago, just for fracturing, is a step-down test. And it's a little different, for fracturing is a step-down test. And this is a little different because, let me describe it before I get into these equations. And I'm going to show you an example. It was a step-down test. I'm not going from above fracturing to below fracturing. I'm always above fracturing. So I am running a test where my rate, I'm reducing rate above fracturing pressure and trying to see what happens. Where, how much change in pressure is going to depend on the condition of the well, the perforations, if there is tortuosity in, around the well bore. If the fracture going straight, say if my perforation are oriented with my, with my, with my fracture orientation and have large number of perforations,


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the fracture going straight, say if my perforation are oriented with my, with my, with my fracture orientation and have large number of perforations, then I don't see a whole lot of pressure drop in perforation. If the fracture is turning around, then you see tortuosity, like what we saw in this example, we looked at before the fracture face may become very rough. So I see a high pressure drop. look bad before the fracture face may become very rough. So I see a high pressure drop. And so by looking at how pressure changing would rate, I may be able to tell the condition of the fracture as it intersects the wood board and if there is something that I need to do to take care of a problem if there is one. So I just want to remind you of this equation here. I just want to remind you of the basic equation. We look at, you know, friction and pipes is something like this. we look at, you know, friction and pipes is something like this, ... Reynolds number of, for fluid flow in, here in pipe.


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is something like this. we look at, you know, friction and pipes is something like this, ... Reynolds number of, for fluid flow in, here in pipe. So, if I have fluid flow in pipe, I, I can create a Reynolds number here, if I have, if I have laminar flow, my friction factor is, is like this. If it's turbine flow, then you need the chart to do it. And, friction inside perforation follows an equation like this, if it's turbine flow, then you need the chart to do it. Friction inside perforation follows an equation like this. I'm not going to go through all those details of the equation, but number of perforation is very important. The diameter of perforation is important. And this discharge coefficient is very important too. Discharge coefficient is very, is very important too. So you're, so I, if I don't have enough perforation, you expect this number to go up very high. So you have very high friction pressure. So the way we look at it, if I go into a step-down test, my pressure drop


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this number to go up very high. So you have very high friction pressure. So the way we look at it, if I go into a step-down test, my pressure drop should be, should look something like this above the top equation. The delta P is equal to some constant times rate raised to some power. And instead of using the equation as is, it is easier to take the logarithm of it. And I say log of delta P, equal to some constant, which is log of A, whatever A is, times that exponent B, times log of rate. So if I plot log of delta P, and you notice that now I need to know, I need to know closure pressure. So this pressure above closure. If I plot the log of delta P versus log of Q, then that is, will give me a straight line. The slope of the straight line will tell me something about the connection between the wood borer and the formation. So if the slope is very high, that usually, if you look back at the equation for perforation, that usually tells me there's not enough perforations. That usually


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is very high, that usually, if you look back at the equation for perforation, that usually tells me there's not enough perforations. That usually does not happen. If it happens, that means one has not designed the fracturing properly. Although we have seen cases, we've seen cases where perforations were not sufficient, that doesn't happen very often. Okay, so if this is the situation, the obvious solution is to go back and re-perforate. Otherwise you'll have a lot of issues in the fracturing treatment. So that you run the test before the fracturing treatment, then you go back and re-perforate. And most of the time, before vertical well you perforate about, the common perforation scheme is six shots per foot, 60 degree facing. If it's fractured horizontal well, then you build a cluster, lots of perforation in a cluster. We did not talk very much about fracturing horizontal wells, but this is another subject that's extremely interesting. We'll not be able much about Fraction Horizontal


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much about fracturing horizontal wells, but this is another subject that's extremely interesting. We'll not be able much about Fraction Horizontal Wells, but this is, this is another subject that's extremely interesting, we'll not be able to cover here, but if you look at, at that book that I, we published, it has very nice chapters, multiple chapters on, actually the whole book is about Fraction Horizontal I'm part of one couple of chapters on the right mechanics part of it. If I get a slope of 0.5 to 1, that may be maybe a tortuous path. Tortuous path meaning that the fracture is turning around, meaning that the fracture is turning around. And, many people have decided, well, if I see that in the, in the test, that tells me that the fracture is, has very rough surface, is turning around. And, what do you do if you have rough surface? You know, if you are a carpenter and you have a rough surface you use sandpaper to smooth it out and that's exactly what people have suggested to use


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You know, if you are a carpenter and you have a rough surface you use sandpaper to smooth it out and that's exactly what people have suggested to use and I'll show a real example with this was exactly used. So you use you inject propant or sand you use, you inject propent or sand, but on slugs, not continuous sand, but you inject the slugs as it goes in, it's essentially smoothens the surface of sand, of the fracture, and it reduces the pressure, the friction pressure. If I have a slope of, let's say of 0.25 or so, around this slope, that usually indication that things are going okay and you can just fracture. When you get into fracture horizontal welds, pressure drop is a lot higher and without any problems. It is the nature of the fracturing and fracturing horizontal words. Maybe in the future we have a lecture on it. This is an example that was published by, I forgot to put the date on it, by Hayden and Stijend. They actually ran a case, they published multiple cases, they were


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that was published by, I forgot to put the date on it, by Hayden and Stijend. They actually ran a case, they published multiple cases, they were looking at testing. And they got fairly sharp slope, so they ran back almost like another test, injecting with slugs or propane, and then they run the step down test and they're very much like what people would expect. The net pressure not only dropped, so you're seeing there's a lot of friction pressure that was removed, not only that, the slope also became flatter. So, that was a very successful situation they, they handled. By the way, Hayden and Stijns are really great people in, in fracturing. I've known them for many years. I've known them for many years. Determination of closure pressure, we sometimes in tests like this, we, if you would use a square root of time graph, that was been idea is, the idea is basically following Carter's equation. So let us talk about the tests that estimation of when you want to estimate, not just the


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idea is, the idea is basically following Carter's equation. So let us talk about the tests that estimation of when you want to estimate, not just the closure pressure, but you want to leak off coefficient, maybe formation probability, poor pressure, all this information. There's a lot of information that one can recover from many frac tests or DFIT. I'm going to talk about the basic stuff. Well, unfortunately we would not have the time or it takes a lot more time to go into all the details. So the original technique that was developed was developed by Nolte, it was ... at the time he was working for Amaco, later on joined Slumber J. And the paper that he wrote is SPE 8341, as I'm writing here. It's really classical paper. ... You... you... I would advise you to read it, although it is not an easy paper to read. I... I have to tell you that, but ... we're going to go through the basic technique here. We'll not go through the derivation, but through the basic technique. But it's an


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that, but ... we're going to go through the basic technique here. We'll not go through the derivation, but through the basic technique. But it's an excellent paper that started all those ideas of testing. Then once Nolte published his paper there was multiple papers afterwards on modification of this technique, updating the technique that is used as g-function derivative analysis. Nolte is the one that came up with g-function but it's not exactly the way people use it right now. We're going to go through both. And so let us talk first about Noltes technique and that will give you an understanding of what he did and then we go further into it. So the original technique was depending on type curve matching to calculate all kinds of parameters. And there was a basic assumption of some fracture geometry. And the technique worked very well. I'm going to give you the final equations for it. The only problem with the technique, as you're going to see, that if you deviate from ideal, ideal


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I'm going to give you the final equations for it. The only problem with the technique, as you're going to see, that if you deviate from ideal, ideal would not tell you why. So in the original technique, without going through the detail of derivation, we do that when we teach a graduate class actually. He developed, Nolte did develop the small g function, which he said, well, this is what you would observe. And that delta is basically dimensionless time. Is when you have a high leak off versus low leak off. And then decided to continue working with the high leak off and then decided to continue working with the high leak off case, saying my G function is, which is capital G now, this is essentially the pressure drop. G function is nothing but dimensionless pressure drop. It is function of this lower G function and we people have used this equation here this is lower case G rather rather than the one raised to power 3 over 2 rather than this equation. And once you do that you end the


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equation here this is lower case G rather rather than the one raised to power 3 over 2 rather than this equation. And once you do that you end the same, this is my equation here. This is very much like what you see in world testing. So I know g function, dimensionless pressure is function of dimensionless time, and the definition of that g, definition of the G function is here. So it is function of height, a constant that depends on the fluid, the Delta P and I'm going to describe you what Delta P is, it's a little different definition than you are used to, if you've done some more testing. A leak off coefficient, then this is the pay zone. So this is height of the fracture versus height of the pay zone where the fluid is leaking off. And so HP is where fluid is leaking off. E prime is like, if you remember what we discussed is Young's modulus divided by one minus square of Poisson's ratio. And the square root of T, that is my injection time. Okay. So if I use this equation I can


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modulus divided by one minus square of Poisson's ratio. And the square root of T, that is my injection time. Okay. So if I use this equation I can actually, it's not difficult to create a curve like, a bunch of curves like this. Well now he has reference time. You look at the equation before, g at some, this is dimensionless time and this is reference time. Okay. And delta P is the difference in pressure relative to reference time. I will describe it in a minute if you want to use it in a problem. So they basically in the original paper by Nolte he used the reference time of 0.25. So for example, if my injection time is 20 minutes, reference time of 0.25 is quarter of that 20 minutes, which is five minutes. So this would be like for five minutes, 10 minutes, 15 and 20. So, he used use the reference, dimension of surface time of 0.25, 0.5, 0.75 and one. And you, once you do that, it's, if you use the equations we just in the previous slide, you can build those curves. So I can, you can


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0.75 and one. And you, once you do that, it's, if you use the equations we just in the previous slide, you can build those curves. So I can, you can build what the curve for 0.25, 0.5, 0.75, 0.5, 0.75 and 1. So it's very easy to build this graph and you plot this data versus delta, which is your dimensionless time. So you can see right away, just to attract your attention, obviously the first reference time is 0.25, you don't have data below 0.25. If it's 0.5, you can don't have data below 0.5. So that's the reason the curves go this way. And so if I, let me see if I probably did not, I probably should have added another graph to show you. So anyway, I can get my data points like this and you can put them very much like what he borrowed these techniques from world testing, if I match the data, the measured data versus the theoretical data, if I match them, then I could pick a match point, which he picked a point where G, the capital G, the initial pressure, is equal to 1 one and pick


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if I match them, then I could pick a match point, which he picked a point where G, the capital G, the initial pressure, is equal to 1 one and pick stuff from the other curve that you called it P star. This is nothing to do with P star you use in well testing, if you are familiar with well testing. Absolutely nothing to do with it. P star in well testing is extrapolation of pressure and maybe average, close to average reservoir pressure. Here it is nothing but a match point corresponding to dimensionless pressure of 1. And so once you do that, once you get P star, here is P star, so this is, North is P star. Once you, you get it, you substitute in this equation, I get Lykov coefficient. So hopefully I know when, I know the heights and I know BS, this is just a constant here depending on N prime. If you remember we talked about fluids last time. So the flow behavior index. And so that I know, I know, hopefully you know Young's modulus and I know P star. I calculate the Lyakhoff


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last time. So the flow behavior index. And so that I know, I know, hopefully you know Young's modulus and I know P star. I calculate the Lyakhoff coefficient. Once I do that, I can go in here, calculate rho. Again, this is corresponding to one another. So if I put this one, this would be P star, and I pick ISIP. I can calculate rho. From rho I get efficiency, fraction efficiency, I calculate fraction length, I calculate fraction width, so everything would, would work well. Okay? Okay, the, the, let me go back to this graph and look at, look at it. So I'm, here we're matching four curves. And you notice that it's very rare that you can match the four curves with the theoretical, with the real data, with the theoretical data. And so you do your best to match, but like here, for example, I see deviation at the beginning, that looks good here, it looks good here, then there's deviation at the end. So that technique does not tell me where there is deviation. So if the deviation are


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here, it looks good here, then there's deviation at the end. So that technique does not tell me where there is deviation. So if the deviation are extreme, you can look at it and say, this may not be useful enough. Okay? So, so people have started looking at it, although it's extremely valuable, they wanna see how to make it even more valuable, to become more useful and to identify all problems that you may see. So people have looked at multiple issues. One issue for example is temperature change. If you're running a test on a very hot formation, and you're monitoring pressure, in a few cases in South Texas, we observed that actually pressure went down and then it started going up again. Well, that does not exactly agree with the theory. So, one thing, I did this work some time ago when we found out that, because pressure is increasing without that is probably due to temperature changes. So we started running tests and observing, measuring not just the pressure, but measuring


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without that is probably due to temperature changes. So we started running tests and observing, measuring not just the pressure, but measuring temperature as well. And we saw the increase in temperature. So we developed the technology to correct for pressure, the effect of temperature on pressure. We're actually applying that similar technology as well as newer technology, obviously, developing technology for ... working on ... geothermal wells. We're... we're starting to analyze wells and geothermal reservoirs where obviously ... the fraction fluid is heating up very much and we observe that same problem. very much and we observe that same problem. And so, another effect is when you have natural fractured formation. So, how you identify what is going on? So, there was an interesting people I referred to earlier by Maharjee and ... and Barry. Margie and Barry. So let's look at their equation. Very, very interesting equation. If you, what they did is if you look at at g function


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and Barry. Margie and Barry. So let's look at their equation. Very, very interesting equation. If you, what they did is if you look at at g function definition, looks that is, that is what Nolte has developed. that is, that is what Nolte has developed. So if you take the derivative, the derivative of pressure with respect to g function, you end the equation like this, then if you say I'm going this by g function. So I multiply here by g, multiply here by g, I end with this equation. And I say, well, if I plot g dp dg versus g function, what should I get? I should be, I should get a straight line going through the origin. You see, the slope of the straight line is here. So the slope of the straight line will give me the leak-off coefficient. So in order to have analyzable data, I need to see with GDPDG versus G-function, I would need to see a straight line going through the origin. So you look at data. data here this is g function this is the gdpdg sitting on secondary axis but you can


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a straight line going through the origin. So you look at data. data here this is g function this is the gdpdg sitting on secondary axis but you can see it is going through basically is going through the origin this is a almost ideal case and so I'm seeing pressure decline, there is fluctuation here, and I see a pressure fluctuation here. As long as we see fluctuation, we need to talk about it a little bit. This is, this fluctuation is nothing but ... essentially water hammer. If you do not know what water hammer is, think about it this way. If I have a fluid say in a very large tank and going through a pipe, where like, like almost connecting to a faucet, like, almost connecting to a faucet. And, when I shut down that faucet, or fluid does not know that it, that the, that water had stopped. So, it actually continues to move, the water continue to move, compressing the, the fluid or the liquid at that faucet, at that closure. ... So it increases, goes above original pressure, then it


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to move, compressing the, the fluid or the liquid at that faucet, at that closure. ... So it increases, goes above original pressure, then it flows back, since pressure had increased there, it has to flow back into the tank, and it keeps going back and forth, and every time the signal decays, till it disappears. So, obviously you do not, you do not see it in your house, although, although even in ... in a house, it could happen. ... Sometimes, if pipes are not held in place, you, you shut down, you shut down ... a faucet, and you hear rattling on pipes. That's exactly the same thing you have here in Water Hammer. It's, there was a test that we did work on and it's a hydraulic impedance testing, was essentially based on this idea by imposing a drop in pressure and observing the signal going through downhole into a fracture, then reflecting back. So, usually when you see water hammer, is an indication of very tight formation. Because if, if, if the formation probability is very high,


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back. So, usually when you see water hammer, is an indication of very tight formation. Because if, if, if the formation probability is very high, then the damping is, is very high too. So you, you don't see that fluctuation. That fluctuation is when you use liquid, and when you have a tight formation. There is techniques to analyze water hammer. And some of them like hydraulic impedance testing, I... I wrote it, there was some work done on the subject several years ago, I... more than 20 years ago, and actually I wrote a paper on subject, where we applied it to calculate fraction length. It's a very interesting technique. But, important thing here, so that does not, the presence of water hammer, does not disqualify the technique we're applying here. So, you can see, you see very nice straight line. So, this is, this is essentially, almost an ideal case. So, if I see situation like this, I can take the slope like this is intersecting the origin, you have a straight line, I can


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almost an ideal case. So, if I see situation like this, I can take the slope like this is intersecting the origin, you have a straight line, I can calculate very much a calculate Lekhov coefficient from that slope. And I can come here and say that this is normally curve there is nothing extraordinary. Okay now there are cases where people have observed when you plot the g function it goes up and then it's flattened out and flattened down then it's eventually follows a straight line. And if I draw the straight line going through the origin, I can calculate leak of coefficient in the formation here. And the ending there, this is where the fracture closed. So, what is going on here? Well, this is at high pressure. If you have natural fractures, basically what we're talking here, fissures, natural fractures existing, you open up those natural fractures, so you have very high leak off into those natural fractures. As the pressure, you see the pressure is declining this way. Well, G-unction


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fractures, so you have very high leak off into those natural fractures. As the pressure, you see the pressure is declining this way. Well, G-unction is increasing. As the pressure declines, those fissures start closing. Eventually, this would, the natural fracture close, but the fracture itself, the hydraulic fracture is still open. So the natural fractures are closed at a higher pressure than the hydraulic fracture, because they're not in the same orientation, basically. So you can, so that here, not only I can get the leak off coefficient from here, but I can say, hey, I have also natural fractures. So that became this, when you see such a behavior, you can diagnose it. Well, sometimes you actually see the reverse behavior. And so you're seeing that eventually follow a straight line that goes through the origin but in the area here I don't have that straight line. So I can calculate the Lekow coefficient here from the formation from this area, but in the earlier area, it usually


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I don't have that straight line. So I can calculate the Lekow coefficient here from the formation from this area, but in the earlier area, it usually interpreted as, the, the fracture is losing, is losing height. And so, if I, if I calculate leak off coefficient from here is, from that early part, that's, that's not work very well. part of this, does not work very well. It's ... another, another ... another area, that or shape that you may see, is where, when you find, here in this specific case, this is a very tight formation, because you have really high, you have a very high water hammer, you can see very sharp water hammer, where pressure has been fluctuating. You look at it here, very severely, and not only that, for a fairly long time. That's an indication of very tight formation. In very tight formation, if I'm, if my, the leak off is, is very small, if the leak off is very small, ... maybe the pressure will equalize inside the fracture, and it stays inside the fracture, at a


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is, is very small, if the leak off is very small, ... maybe the pressure will equalize inside the fracture, and it stays inside the fracture, at a higher than fracturing pressure for some time. So, what happens when the fracturing, the fluid pressure inside the fracture, it stays for some time above fracturing pressure? When, what happens is, and without leaking off, very much, very little leak off, the fracture will continue to propagate, even after you stop injection. And, you can see in this case, when you draw that straight, you draw that straight line, the straight line never ended in this case. Has not ended yet, so your fracture has not closed yet, and you can see it does not intersect the origin, the zero and zero. So, it's sitting above zero and zero. So I, that leak of coefficient, the closure time obviously is very long and fracture has not closed yet. And the, the fracture tip extension after end of injection combined with the water hammer that we're seeing here, it tells


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has not closed yet. And the, the fracture tip extension after end of injection combined with the water hammer that we're seeing here, it tells me that the formation is extremely tight. It may not be even be productive. There was a lot of newer technology that came up afterwards. The first attempt to calculate permeability was by Mayer Hoffer. I should have put his reference here. as referenced here. And basically, they try to do superposition and calculate fracture length, and formation permeability, especially formation permeability from before closure, rather than calculating leak-off coefficient. before closure rather than calculating leak-off coefficient. Then the issue with that original technique, although it's a very smart idea, the issue with it was you have to be very close to the right solution in order, if it was an iterative technique, in order for those iterations to converge. So you, so that was a problem. Valco and Economidis came back and they published a very


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technique, in order for those iterations to converge. So you, so that was a problem. Valco and Economidis came back and they published a very interesting paper, they, they presented a very good technique for calculation of formation permeability. So it is update over Mayor Hafer and the Economists, Michael Economists. Then we saw an issue with it, there was some issues with the technique, with oversight in some of the definitions, so we have corrected that, and Lamy and I published a paper on the subject. So I would advise you to, if you apply VALCON to convey this technique, please read the paper by Elami and I, because you need to consider that correction. It's an oversight on VALCO and the Convenience, or maybe in typing. Then we published another technique that came up in 2014, where we can ... Sadiq and I, we went through, rather than going, I may show you a question from Valko, and we can read this in a minute, or, or it's going to be on the slides that I will put in, on


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than going, I may show you a question from Valko, and we can read this in a minute, or, or it's going to be on the slides that I will put in, on ResearcherGate. Rather than going through the superposition way of, and depending on the fractioning equations, what we did, we developed Sadiq and I, Sadiq in his PhD dissertation, he developed the equation rigorously of fluid flow with fracture propagation, and based on pressure decline, and we, we came up with a technique, that rather than calculating permeability, we, it calculates fracture dimensions, fracture size. So fracture area. So it, it requires, it requires maybe, what combining the technique either with Valkyrie's technique or with after closure technique that we'll describe in a second. ... There is a recent ... approach by McClure, it's not for formation probability, but basically for ... closure pressure. ... Closure pressure, there is a lot of controversy, how high or how low it is and, ... so McClure found, he developed


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for ... closure pressure. ... Closure pressure, there is a lot of controversy, how high or how low it is and, ... so McClure found, he developed developed an approach based on, on fracturing. And, he predicts that, that, that closure pressure is a lot higher than what you get from G-Function. We, another technique that was ... been developed and being developed, we are using, this we are doing it at ... UH. We used the wavelet transform ... to, to calculate closure pressure. ... wavelet is, is a, is a, is an approach, or it's data signal analysis basically. ... And it maintains the, or tell you the discontinuity, or the issues with, with the signal, ... when it maintains the, the location and time. So when we applied it, we actually we find out that closure pressure in many cases is indeed higher than what G-Function would predict. So it happens earlier in time, but it's not as high as what McClure has published. We are having a paper in, coming in February, where we are going to


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it happens earlier in time, but it's not as high as what McClure has published. We are having a paper in, coming in February, where we are going to compare the, the various techniques. ... For after closure analysis, for permeability, there is two basic technique, well actually there's several techniques, but to me they are, the basic techniques are the one developed by Nalti and the one I, I published back in 2005, but we upgraded the technique later on. ... Essentially, Nour... was noticed technique, he's look at it saying, I have a constant pressure injection and I either have radial flow or linear flow. And ... it, it works, it works okay, but I think what we, what we are, what we presented in ALMA is a little different approach. Rather than saying is a constant pressure, we look at it as a total volume that was injected, since it's over a shorter time than the, than the, than the after closure time, or actually after injection time. And if you, if you look at it that fashion, and


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a shorter time than the, than the, than the after closure time, or actually after injection time. And if you, if you look at it that fashion, and put the equation together, you end up finding an approach where, when you plot the data the way we are saying here in the paper in 2005, you can tell whether you have linear flow, radial flow, bilinear flow, or even spherical flow. Actually, we have seen all those flow regimes. But, so that, the technique actually, the advantage of it, rather than you try to find a certain slope, or you plot it, you make assumption of the slope, or of the flow regime, the technique first, the first graph graph tells you what flow regime you have and based on that flow regime you continue, so you... you move from determining the flow regime into different direction depending of what flow regime you have and you can then from there you calculate formation, permeability and so on and so forth. The... when we... then we ended developing looking at ... dual


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you can then from there you calculate formation, permeability and so on and so forth. The... when we... then we ended developing looking at ... dual porosity model. ... Because, once we got into shale, we start observing that the behavior is different, so we... we developed ... a couple of techniques, the first techniques with, with observation of the dual porosity model with people, with published in 2009, then with one of my students, Elwaziri, he did very good piece of work on, on dual porosity model where we developed the equation to describe the model in a special way and this way we could analyze the data and we tell formation properties. That is basically the end of this lecture. I'm going to... there is ... to go into other techniques in details, maybe this is something we can do it in the future in a special presentation, but it would require knowledge of well testing to get into more details of testing. So now we'll... Okay, so thank you, doctor, for this informative


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but it would require knowledge of well testing to get into more details of testing. So now we'll... Okay, so thank you, doctor, for this informative session. Now we will begin by addressing some questions. The first question is that from the well-testing techniques we have today, what are the most common techniques used in fracturing shale plates? Say it again, the most common technique, well-testing, what did you do in well-testing? Yes, we have some well testing techniques today. What are the most commonly ones, common ones we see in while fracturing shale plates? A common technique for analysis of data or fracturing itself? He didn't mention but I think analysis. Dr. Salman, I believe the question is, do we use the same well testing techniques we had today in the lecture in fracturing shale plates? Well, that's a very good question. I don't, some people do, I don't advise using exactly the same techniques because shell is naturally fractured, that's number one, is extremely tight


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I don't, some people do, I don't advise using exactly the same techniques because shell is naturally fractured, that's number one, is extremely tight and I have seen people, some people using the will testing techniques blindly. I think that's a bad idea. We've published some papers that goes into details of that and describes. I have especially a review paper in Elsevier that goes into testing of shale in details. And it's a review paper so it goes into a bunch of things. I did not refer to it here, but I would advise the person that asked this question to read that paper, because applying well-testing techniques to defeat applying well-testing techniques to defeat blindly can give you questionable results. Okay, thank you. And the last question for today is that what is... Just one second. I'm going to put... I can't put the paper itself in the presentation because it's a copyrighted, you know, once you publish a paper it's copyrighted, you can't, but I'm going to put the reference


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in the presentation because it's a copyrighted, you know, once you publish a paper it's copyrighted, you can't, but I'm going to put the reference in it and maybe a couple of sentences so you have to get the paper on your own. you, you have to get the paper on your own. Yes, yes. Okay, so the final question for today is that, what is a good software that can be used for well testing, hydraulic, hydraulic fractured wells? it was? I cannot recommend software that is a commercial thing to there's a lot of software that are good I can't I cannot be endorsing a software. We at University of Houston, we have multiple software that we use for analysis of data, as well as we have developed our own software to do certain things that are not used. For example, a wavelet analysis that we developed our own software to do it. And we give it to companies that sponsoring our research. Some of the analysis technique, we developed a spreadsheets to do it since we want to do it a little differently.


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that sponsoring our research. Some of the analysis technique, we developed a spreadsheets to do it since we want to do it a little differently. But several companies have software, they are all very good. I have to decline answering this more than that. Yes, yes, I understand. Thank you. And I have to decline answering this more than that. Yes, yes, I understand. Thank you. Thank you again for the time you have dedicated for delivering this course. And as a reminder, don't forget to do the last quiz for this course and do the final exam, which will be held on Tuesday, the 3rd of November, 2 p.m. Egypt time and also 8 p.m. Egypt time. And also we have another exam Wednesday, the 4th of November, 2 a.m. Egypt time. However, you can only do one final exam with that We have came we have come into a to end and the best of luck and Have a nice day and see you in future webinars. Thank you. Well, thank you everyone and If you if you have Special question Don't hesitate to send me an email at


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day and see you in future webinars. Thank you. Well, thank you everyone and If you if you have Special question Don't hesitate to send me an email at mysolomon.uh.edu. And thanks everyone.


