A COMPREHENSIVE STUDY OF HYDRAULIC FRACTURING TREATMENT DESIGN RESULTING AN IMPROVED PROPPANT SCHEDULING METHOD
A Thesis written by: Kevin Wiradi 12212086
Submitted in partial fulfillment of the requirements for the degree of BACHELOR At the Department of Petroleum Engineering Faculty of Mining and Petroleum Engineering Institut Teknologi Bandung
PETROLEUM ENGINEERING DEPARTMENT FACULTY OF MINING AND PETROLEUM ENGINEERING INSTITUT TEKNOLOGI BANDUNG 2016
A COMPREHENSIVE STUDY OF HYDRAULIC FRACTURING TREATMENT DESIGN RESULTING AN IMPROVED PROPPANT SCHEDULING METHOD
By: Kevin Wiradi NIM: 12212086
Petroleum Engineering Department Institut Teknologi Bandung
Approval: Supervisor Bandung, ____________________
___________________________________ (Prof. Dr. Ir. Sudjati Rachmat, DEA) 195509021980031005
A COMPREHENSIVE STUDY OF HYDRAULIC FRACTURING TREATMENT DESIGN RESULTING AN IMPROVED PROPPANT SCHEDULING METHOD Kevin Wiradi1, Sudjati Rachmat2 1 2
Student of Petroleum Engineering, Institut Teknologi Bandung, Indonesia Lecturer of Petroleum Engineering, Institut Teknologi Bandung, Indonesia
Abstract Back to fracturing history, the first commercial hydraulic fracturing may be done since 1949, but actually the idea of fracturing formation to quicken the production already exist since 1865. So the idea is more than a century old now. Hydraulic fracturing treatment design is one of an aspect that has been developed so much, until now people are able to generate a treatment design without consume much so time on that. Hydraulic fracturing treatment design has been vastly developed since 1953, until in the 2000s Gu, H. et al. has developed a method which includes numerical calculations and then automatically designs the hydraulic fracturing treatment to its most optimum option, and just needs to be told how far would the fracture go, and do it with what fluid and proppant. By the creator its named as Pump Schedule Generator (PSG). But far before that, in 1983 H. R. Crawford developed a methodology with a few calculations to calculate the volume of fracturing fluid needed based on the designed and desired fracture network dimensions, number of proppant needed, and also the production increase. This work analyses the comparison between the older method and PSG, and then modifies the schedule created by the older method to come up to the results of the PSG. A fracturing design simulator, FracCADE 5.1. was used in this study. It helps the writer to understand the basics of Pump Schedule Generator and the causes and effects of parameters to the EOJ result values. The formation’s structure and parameters were taken from an Indonesian shale gas reservoir. Keywords: hydraulic fracturing, Hydraulic Fracturing Treatment Design, schedule, Pump Schedule Generator Sari Kembali ke sejarah perekahan, perekahan hidrolik komersial pertama mungkin telah dilakukan pada tahun 1949, tetapi sebenarnya ide untuk merekahkan formasi untuk mempercepat produksi telah ada sejak 1865. Maka ide ini telah berumur lebih dari satu abad sekarang. Desain penanganan perekahan hidrolik adalah salah satu aspek yang telah dikembangkan sangat besar, hingga sekarang orang-orang dapat menghasilkan desain penanganan tanpa membutuhkan waktu yang banyak untuk hal tersebut. Perekahan hidrolik telah banyak berkembang sejak 1953, hingga pada tahun 2000-an Gu, H. et al mengembangkan sebuah metode yang memiliki perhitungan numerik dan dengan otomatis mendesain penanganan perekahan hidrolik hingga opsi yang memungkinkan dan paling optimum, dan hanya butuh data input mengenai seberapa jauh rekahan akan berpropagasi, dan dilakukan dengan fluida dan proppant yang mana. Oleh pengembangnya dinamakan sebagai Pump Schedule Generator (PSG). Tetapi jauh sebelum itu, pada tahun 1983 H. R. Crawford mengembangkan sebuah metodologi dengan beberapa perhitungan untuk menghitung volume fluida perekah yang berdasar kepada dimensi rekahan yang didesain dan diinginkan, jumlah proppant yang dibutuhkan, dan juga peningkatan produksi. Pekerjaan ini menganalisa perbandingan antara metode yang lama dengan PSG, dan kemudian memodifikasi jadwal yang dibuat oleh metode lama tersebut agar dapat lebih mendekati hasil dari PSG. Simulator desain perekahan, FracCADE 5.1 digunakan untuk studi ini. Software ini membantu penulis untuk mengerti mengenai dasar-dasar Pump Schedule Generator dan sebab akibat dari parameter – parameter yang dapat didesain terhadap nilai – nilai fracture di End of Job. Data mengenai formasi didapat dari salah satu shale gas reservoir di Indonesia. Kata Kunci: perekahan hidrolik, Desain Penanganan Perekahan Hidrolik, jadwal, Pump Schedule Generator
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I. Introduction Back to fracturing history, the first commercial hydraulic fracturing may be done since 1949, but actually the idea of fracturing formation to quicken the production already exist since 1865. So the idea is more than a century old now. Hydraulic fracturing treatment design is one of an aspect that has been developed so much, until now people are able to generate a treatment design without consume much so time on that. Hydraulic fracturing treatment design has been vastly developed since 1953, until in the 2000s Gu, H. et al. has developed a method which includes numerical calculations and then automatically designs the hydraulic fracturing treatment to its most optimum option, and just needs to be told how far would the fracture go, and do it with what fluid and proppant. By the creator its named as Pump Schedule Generator (PSG). But far before that, in 1983 H. R. Crawford developed a methodology with a few calculations to calculate the volume of fracturing fluid needed based on the designed and desired fracture network dimensions, number of proppant needed, and also the production increase. This work analyses the comparison between the Crawford’s method and PSG, and then modifies the schedule created by Crawford’s method to come up to the results of the PSG. A comprehensive reasoning between each differences in each generated schedule is also given in this text. Fracturing model used in this text is KGD, instead of PKN. Between those two models, KGD is more simple than PKN, because the proppant concentration distribution only differs in an axis, so a more quantitybased approach study can be obtained. Fracturing design simulator, FracCADE 5.1. was used in this study. It helps the writer to understand the basics of Pump Schedule Generator and the causes and effects of parameters to the EOJ result values. The formation’s structure and parameters were taken from an Indonesian shale gas reservoir.
Development of Hydraulic Fracturing Treatment Design The first commercial hydraulic fracturing treatment was in 1949, but the first noticed study about schedule design was in 1957 by Howard et. al, 1975 by Harrington et al, then later on followed by Crawford in 1983, Nolte in 1986, and in 2000 by Gu, H. et al. There are 5 paper which writer noticed about the development of hydraulic fracturing treatment design since the first commercial hydraulic fracturing treatment.
1957: 1957: Howard, et. al: “Optimum Fluid Characteristics for Fracture Extension” 1973: Harrington, et. al: “Prediction of the Location and Movement of Fluid Interfaces in a Fracture” 1983: Crawford, H. R.: ”Proppant Scheduling and Calculation of Fluid Lost During Fracturing” 1986: Nolte, K. G.: “Determination of Proppant and Fluid Schedules from Fracturing-Pressure Decline” 2003: Gu, H. et. al: “New Pump Schedule Generator for Hydraulic Fracturing Treatment Design” Harrington et al. presented in the study selection of final proppant concentration based on the fracture conductivity needed to meet design requirements. Then the value of proppant concentration and fracture penetration requirements will be the inputs to a computer program to determine the fluid volume required, amount of proppant and pad volume needed, and proppant addition schedule. Crawford presented the same scope of study with an addition of fluid loss volume to be calculated. A few simple equations, few suggestion steps, and also case problems were given as the outcome of his study to help fracking operators to calculate and generate their own schedule based on the desired fracture geometry. By the time he presented his study, about hundreds of well have been tested by the method. Three years after Crawford there was Nolte who introduced proppant and fluid schedule determination by observing fracturing pressure decline. But the method was said to be applicable primarily for new prospects where little information about about the fracturing response is known. Lastly, Gu et al. presented a pump schedule generator (PSG), which is an automatic proppant and fluid schedule determination by numerical iteration. Gu et al. published the work while they were in Schlumberger back in 2003, which is most probably the one that is used in Schlumberger’s FracCADE ver. 5.1. Two of them will be used, practiced, and discussed in this study, which are Crawford’s method and the Pump Schedule Generator. Crawford’s method was thought to be one of the simplest quantitative method that’s available at the time. The method is based on the leak-off coefficient value and the dimension of the designed desired fracture network to determine the volume of fracturing fluid needed. Although it is quantitative and based on laboratory works on attempt to determine the leak-off coefficient, the method still use 50% of safety factor applied to the pad volume needed to frac the formation until they got the desired fracture dimension. So actually the method is not that deterministic. But still,
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the schedule produced by this method is easy to be produced and also easy to be done. Pump Schedule Generator is the next batch of the hydraulic fracturing treatment design generation. To design a pump schedule more efficiently and effectively, the automatic generation of pump schedule by a computer program is highly desirable. The automatic pump schedule generation is an inverse problem, in which the fracture length and concentration distribution inside the fracture are specified input, whereas the fluid volume and proppant concentration in the pump schedule are to be determined. Problem Statement By doing a lot of background studies, writer take two problems that can be evaluated, there are: 1. What are the differences between the schedules created by Crawford’s hydraulic fracturing treatment design method and Pump Schedule Generator method? 2. Can the schedule result by Crawford’s hydraulic fracturing treatment design method be simply improved? If it’s possible, how are the comparison between the schedule produced by improved Crawford’s method and PSG?
Figure 1 - Methodology of the Study
II.
Theory
Hydraulic Fracturing Basics Hydraulic fracturing is one of well-stimulation technique that is most suitable to wells in low-moderate permeability reservoir. The idea is to create a highly conductive pathway to produce the insitu fluid faster than pre-job condition.
Objectives of This Study The writer then generated two objectives based on the problem stated: 1. Examine the quality comparison of two hydraulic fracture treatment design methods and analyse them, between one suggested by Crawford (1983), and the automated version (Pump Schedule Generator), based on EOJ values (fracture length, height, width, net pressure, conductivity, FCD) and the proppant distribution in the fracture. 2. Observe the values exerted by the improved method with comparison to the earlier method and the automated method. Methodology Since the scope of this study is only about schedule of hydraulic fracturing treatment, the treatment fluid and proppant selection won’t be optimized. Writer only choose them by selecting which is probably the best suited to the formation without doing sensitivity study about it. The methodology of this study is explained in the next figure:
Hydraulic fracturing treatment design is highly affected by the formation parameters, which are type of the encountered formation, formation’s mechanical properties (Young’s Modulus, Poisson’s Ratio), insitu stress, and also the depth of the formation. Formation Mechanical Properties Young’s Modulus This parameter relates the force that is work upon a substance to the length difference between the original length and the resulted length. The equation is as follows: 𝐸=
𝐹 𝐴0 ∆𝐿 𝐿0
𝐹𝐿0
=𝐴
0 ∆𝐿
(1)
Where: E = Young's modulus (modulus of elasticity) F = force exerted on an object under tension A0 = actual cross-sectional area through which the force is applied ΔL = amount by which the length of the object changes L0 = original length of the object Young modulus is highly related to material’s brittleductile attribute. The higher the Young’s modulus value, more forces are needed to extend the material’s length to the same value. It means higher Young modulus value indicates that the substance is able to
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resist more deformation which is made by a working force. Thus, materials with high Young’s modulus value is considered as brittle materials.
𝑎𝑥𝑖𝑎𝑙
𝑥
𝑑𝜀
𝑥
(2)
Where: = resulting Poisson’s ratio = transverse strain (negative for axial tension, positive for axial compression) = axial strain (positive for axial tension, negative for axial compression)
𝑣 𝜀𝑡𝑟𝑎𝑛𝑠 𝜀𝑎𝑥𝑖𝑎𝑙
Figure 2 - Young's Modulus compares the strain and stress that occur over a material (www4.ncsu.edu)
𝑑𝜀𝑦
𝑑𝜀
𝑣 = − 𝑑𝜀𝑡𝑟𝑎𝑛𝑠 = − 𝑑𝜀 = 𝑑𝜀 𝑧
Most materials have Poisson’s ratio values ranging between 0.0 and 0.5. A perfectly incompressible material deformed elastically at small strains would have a Poisson’s ratio of exactly 0.5. Sand’s Poisson ratio is ranged between 0.20 and 0.45, while clay’s range is a lot smaller, ranged between 0.30 and 0.45.
In the opposite, low Young modulus value means the substance is able to deform easily by lower value of working force. Rubber is the example of a substance which has a low Young Modulus value. Thus materials with low Young’s modulus value is considered as ductile materials. Their difference can be explained in the stress-strain curve below (Figure 3).
Figure 4 - Poisson effect when a material is being strained (en.wikipedia.org)
Figure 3 - Stress - strain curve for brittle and ductile materials (mechanical-materialstechnology.blogspot.com)
The breakdown characteristic of brittle and ductile materials is different. Brittle materials are not elastic, thus right after the breakdown stress is achieved, the material will be broken instantly. It’s different with the ductile materials, they are not broken instantly after a certain stress is acted upon them. Instead, if the stress passes a critical value, the material will be deformed permanently, and the breakdown stress is usually much higher than the brittle one. Poisson’s Ratio This parameter is the negative ratio of transverse to axial strain. When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular to the direction of compression. This phenomenon is called the Poisson effect. The equation is as follows:
This Poisson effect has a role in hydraulic fracturing treatment design. Poisson’s ratio value is used in horizontal stress calculations, as it is also affected by the deformation which is caused by the overburden pressure (vertical axis). Stresses Acting upon Reservoir There are two dimension of stresses acting upon a reservoir, vertical and horizontal stress. Vertical Stress Two factors affecting the vertical stress which is counted for calculating reservoir mechanical behavior are overburden pressure and reservoir pore pressure. Consider a reservoir rock at depth H, the in situ stress caused by overburden formation in the vertical direction is expressed as: 𝜎𝑣 =
𝜌𝐻 144
(3)
Where: 𝜎𝑣 = overburden stress, psi 𝜌 = average density of overburden formation H = depth of formation
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Then the contact stress between grains is called effective stress: 𝜎𝑣′ = 𝜎𝑣 − 𝛼𝑝𝑝
normal to the least principal stress. That is why, the working stress in both axis determines the fracture orientation.
(4)
Where: 𝜎𝑣′ = effective vertical stress, psi 𝛼 = Biot’s poro-elastic constant, approximately 0.7 𝑝𝑝 = pore pressure, psi Figure 5 below explains the concept of effective stress between grains.
Depth of the formation also determines the fracture orientation. The deeper the reservoir, the overburden stress value will be higher. Thus, the vertical stress will be more dominant and make a vertical-oriented fracture instead of horizontal-oriented one. Based on a study in a field, the critical depth which changes the fracture orientation is about 600 meters. It means, if an operator fractures a formation less than 600 meters deep, he will get a horizontal fracture. Deeper than that he will get a vertical fracture.
Figure 5 - Correlation between effective vertical stress and pore pressure (Guo, 2007)
Horizontal Stress The effective horizontal stress is expressed as: 𝑣
𝜎ℎ′ = 1−𝑣 𝜎𝑣′
(5)
Where v is Poisson’s ratio. The effective horizontal stress is caused by the overburden force acting upon the grains in the reservoir. The total (minimum) horizontal stress is expressed as 𝜎ℎ = 𝜎ℎ′ + 𝛼𝑝𝑝
(6)
Total horizontal stress is still excluding tectonic stress. Thus, it’s said to be the minimum value of the horizontal stress. The maximum horizontal stress may be: 𝜎ℎ,𝑚𝑎𝑥 = 𝜎ℎ,𝑚𝑖𝑛 + 𝜎𝑡𝑒𝑐𝑡
(7)
Terzaghi presented following expression for the breakdown pressure: 𝑝𝑏𝑑 = 3𝜎ℎ,𝑚𝑖𝑛 − 𝜎ℎ,𝑚𝑎𝑥 + 𝑇0 − 𝑝𝑝
(8)
Where T0 is the tensile strength of the rock.
Figure 6 - Fracture orientation determined by direction of the least working stress (Schechter, 1992)
Hydraulic Fracture Treatment Design Hydraulic fracture schedule is one of the keys to successfully run a fracking job, as the operator has to determine which fluid is going to be used to deliver which proppant, and when the fluid to be pumped to the downhole with how much concentration of proppant. And finally, how would the fracture face be far in the target depth. All of the mentioned above has to be designed carefully to deliver the best production scenario. A few pictures to depict the fracturing activity are in the Figure 7. Basically, the treatment’s function is to give enough hydraulic pressure to make the bottomhole pressure pass the formation breakdown pressure to frack the reservoir up to a certain radius from the wellbore. Then a certain number of pressure, called fracture propagation pressure, is to be maintained to enlarge the fracture.
Fracture Orientation The orientation of a fracture in earth’s body is determined by the stress values in the two axis. It is postulated that fractures should occur along planes
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Figure 8 - Pressure profile against time in a typical hydraulic fracturing treatment (Schechter, 1992)
At pad stage, operator pumps a certain volume of treatment fluid to the wellbore, to give sufficient hydraulic pressure to frack the formation. After the operator propagates the fracture up to a desired radius, then the frack is kept open at the instantaneous shut-in pressure. Then the slurry stage begins. The slurry being injected consists of the selected treatment fluid with proppants mixed in it. The goal of the slurry stage is to take the proppants into the formation and spread the proppants evenly in the reservoir.
Figure 7 - Stages of hydraulic fracturing treatment (Guo, 2007)
After that a lower value of pressure, instantaneous shut-in pressure, is then to be maintained to keep the fracture from closing. A graphic in Figure 7 shows a pressure profile versus pumping time in a typical hydraulic fracture treatment. The next procedure is to put proppants into the fracture to keep the frack from a complete closure. The proppant also has to meet some specific requirement, related to the formation closure pressure. If the proppant cannot withstand the closure pressure, the proppant will be shattered and cannot give its best conductivity. A few problems would be encountered if the fractured formation is too soft. The proppant would be embedded into the fracture surface, so the fracture width will be smaller than it should be. Stages in Hydraulic Fracturing Treatment Commonly in a hydraulic fracture treatment, there are 3 main stages, pad stage, slurry stage, and flush stage. These stages are related to a graph in Figure 8.
After the proppants is set, there is a flush stage. Flush stage has a goal of cleaning up the fracked reservoir and the wellbore from all unwanted substance except the proppants.
Treatment Fluid Fluids that is used during fracturing has to pass a few selection process to evade a screen out (failed operation) or gel damage (failure at post-operation). A few criteria that has to be considered to select a treatment fluid are as follows: Viscosity, this parameter affects the fluid’s ability to frack the rock and brings proppant to the fracture area in the fractured rock. Fluid Loss, this parameter is one of major design variables of fracturing fluid, measured by fluid-loss coefficient (CL) and spurt loss (SP). Operator of hydraulic fracture treatment jobs doesn’t want excessive fluid loss since it will cause the fracture won’t propagate further if the fluid supplied and accumulated to the downhole is insufficient. So, a
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fracture fluid with the lowest possible value of fluidloss (leak-off) coefficient CL should be selected. Fluid efficiency, this parameter’s value shows the portion of fluid that is still in the fracture area at any point in time, when compared to the total volume injected at the same point in time. If too much fluid leaks off, the fluid has low efficiency (10 – 20%), and the created fracture will be only a small of the total volume injected. However, if the fluid has high efficiency (80 – 90%), the fracture will not close rapidly after the treatment. Ideally, a fluid efficiency of 40 – 60% will provide an optimum balance between creating the fracture and having fracture close down after the treatment. Fluid compatibility, this parameter also has to be considered especially in formation sensitive to clay swelling, emulsion, fines migration, which lower the chance of production success after the operation is run. It is better to test a core from the formation with the fracturing fluid in the lab first to check its compatibility to the rock.
formation depends on the kind of material of the proppant itself. Many materials including glass beads, walnut shells, plastic beads, and aluminum pellets have at one time or another been used to prop hydraulic fractures. As the fracture fluids have improved, the number of different materials used has steadily been reduced. Presently, sand and bauxite are in common use. Sand has proven to be successful as a proppant for all types of reservoirs, and it is less expensive than other types of proppant as it can be found anywhere near aquatic environment (i.e. shore, seabed). Sand for use as proppant should not contain more than 5 wt% fines which, if present in excessive quantities, reduce the fracture conductivity. Sand has the additional advantage that when crushed, it breaks into smaller fragments, rather than being powdered. This particular advantage helps to maintain high fracture conductivities even when the closure stresses supported by the proppant are large. Sintered bauxite
Stability, the fracturing fluid also has to be not sensitive to temperature. Because the formation’s temperature will be escalated especially in the deeper formation. If the available fluid is not compatible in temperature stability, an additive called High Temperature Stabilizer can be added to ensure the fluid stability in the reservoir.
A high-strength proppant, which does not crush as readily as sand under high closure stresses. Bauxite is denser than sand, and thus the fracture fluid designed to transport bauxite will have to be more viscous and hence more expensive than a fluid that will transport sand. So the treating pump pressure also has to be bigger than when transporting sand proppants.
Friction Pressure, this parameter is considered as critical. An excessive friction pressure caused by the treatment fluid will decrease the maximum effective bottomhole pressure by the same pumping unit. Therefore, the friction has to be calculated along the hydraulic fracturing treatment design with the limitation of pumping pressure.
Ceramics
Economical, all of the parameters above leads to economical aspect of the selected treatment fluid, will the treatment fluid fits the bill after the design is completed. The economical aspect is not only considered from the price of the treatment fluid, but the fold of increase created by the hydraulic fracturing operation also has to overcome the expenses of the hydraulic fracturing operation. Inexpensive fluid which causes gel damage most of the time will not be selected if a better fluid is available, even though it’s several times more expensive.
Both of them are stronger in stronger closure stress than their respective base proppant (sand or ceramics). But the permeability profile of them both are slightly lower in the low closure stress zone. It shows that the resin closes the space between the proppant more tightly than before. Thus, when the closure stress is low, the permeability of them both are not affected by the strength of the proppant. But at the higher closure stress zone, resin coated sand/ceramics shows more integrity.
Proppant
As we can see from the graphs, permeability of the resin coated proppants (for both type) will pass the respective base proppant at certain closure pressure (sand = 3500 psi, ceramic = 7200 psi).
Proppant’s purpose to be used in hydraulic fracturing treatment is to prop/support the fractured area after it is created. Its strength against the closure pressure of the
Currently it is widely used, as it is the only alternative that is given by FracCADE 5.1 other than sand type proppants. It is even more stronger than sintered bauxite. Resin-coated Sand/Ceramics
The characteristic of each type of proppant can be seen in Figure 18. Note from the figure: Red = Sand; Green = Resin-coated sand; Blue = Ceramic; Purple = Resincoated ceramic
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Fracture Geometry (Model) There are still some controversies about whether a single fracture or multiple fractures are created in a hydraulic fracturing job. Both cases have been evidenced based on the information from tiltmeters and microseismic data, it is commonly accepted that each individual fracture is sheet-like. However, the shape of the fracture varies as predicted by different models.
PKN model was firstly derived by Perkins and Kern (1961) for a fixed-height vertical fracture, then Nordgren (1972) added leakoff and storage within the fracture (due to increasing width) to the Perkins and Kern model, which is shown in the Figure 11. It is important to emphasize that even for contained fractures, the PKN solution is only valid when the fracture length is at least three times the height.
Currently, the most widely used fracture geometry are PKN and KGD models, as they are simple enough to be created or modeled. But before that, a simple radial crack/fracture model was first presented by Sneddon and Elliot (1946) called a Radial Fracture Model. This occurs when there are no barriers constraining height growth or when a horizontal fracture is created.
Figure 9 - Radial (penny-shaped) fracture geometry (www.intechopen.com)
KGD model assumes that a fixed height vertical fracture is propagated in a well-confined pay zone (i.e., the stresses in the layers above and below the pay zone are large enough to prevent fracture growth out of the pay zone). This model was presented by Khristianovich and Zheltov (1955) as shown in the Figure 10. The model assumes that the width of the crack at any distance from the well is independent of vertical position, which is a reasonable approximation for a fracture with height much greater than its length.
Figure 11 - PKN fracture geometry (Guo, 2007)
The three models discussed before all assume that the fracture is planar, that is, fracture propagates in a particular direction, fluid flow is one-dimensional along the length of the fracture, and leakoff behavior is governed by a simple expression derived from filtration theory. Those planar 2D models are deviated with significant simplifying assumptions. But they are helpful enough for understanding the growth of hydraulic fractures. Currently modern computer allows routine treatment design to be made with more complex models, which are solved numerically. Then pseudo-threedimensional models were invented. There are two types of P3D model, there are lumped and cell based. In the lumped models, the fracture shape is assumed to consist of two half-ellipses joined at the center. The horizontal length and wellbore vertical tip extensions are calculated at each time-step, and the assumed shape is made to match these positions. In cell-based models, the fracture shape is not prescribed. The fracture is treated as a series of connected cells, which are linked only via the fluid flow from cell to cell. The height at any cross-section is calculated from the pressure in that cell, and fluid flow in the vertical direction is generally approximated. Productivity of Fractured Wells
Figure 10 - KGD fracture geometry (Guo, 2007)
After the reservoir is fractured, the altered permeability of the fracture will escalate the production rate highly. The relative importance of each of the steps can be
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analyzed using the concept of fracture conductivity defined as: 𝐹𝐶𝐷 =
𝑘𝑓 𝑤
(9)
𝑘𝑥𝑓
Where: FCD = fracture conductivity, dimensionless kf = fracture permeability, md w = fracture width, ft xf = fracture half-length, ft. If the fracture is considered as a negative skin where the fractured area is much less than the drainage area of the well, the long term productivity of the fractured well can be estimated assuming pseudo-radial flow in the reservoir. Then the inflow equation can be written as: 𝑞=
𝑘ℎ(𝑝𝑒 −𝑝𝑤𝑓 ) 𝑟 141.2𝐵𝜇(ln 𝑒 +𝑆𝑓 )
(10)
𝑟𝑤
Where Sf is the equivalent skin factor, with negative sign indicating that the wellbore is stimulated. The fold of increase can be expressed as: 𝐽 𝐽𝑜
=
𝑟 ln 𝑒
𝑟𝑤 𝑟 ln 𝑒 +𝑆𝑓 𝑟𝑤
𝐽𝑜
𝑟 3 0.72 (ln 𝑒 − +𝑆𝑜 )
=
(𝑧𝑒 √𝑐+𝑆)(
Proppant Scheduling Technique Crawford’s Proppant Scheduling and Calculation of Fluid Lost Crawford suggested a method that determines two parameters that has to be calculated:
(11)
But when the fracture dimension is comparable to the drainage area of the well, significant error may result from using the equation, which was derived based on radial flow. An analytical solution for estimating fold of increase in well productivity for a fractured reservoir was presented by Guo and Schechter (1999) as follows: 𝐽
Figure 12 - A method to determine fractured skin based on dimensionless fracture conductivity value (Guo, 2007)
𝑟𝑤 4 1 1 ) − √𝑐𝑥𝑓 2𝑥𝑓 √𝑐 1−𝑒
(12)
Amount of fracturing fluid needed without wasteful overdesign, and Efficient proppant schedule which simultaneously provides high fracture conductivity, long propped lengths and low odds of a screenout. The approach presented here to achieve a few goals for highly viscous or crosslinked, fracturing fluids is to: 1. Estimate the created fracture area: 𝑉
𝐴 = 𝑊+3𝐶𝑇0.5
(14)
Where: 𝑐=𝑧
2𝑘
𝑒 𝑤𝑘𝑓
(13)
And ze is the distance between the fracture and the boundary of the drainage area. One of the method to determine skin factor is using Figure 12 below. McGuire-Sikora developed a chart in Figure 19 to predict a hydraulic fractured reservoir’s skin based on the permeability before-after treatment, well spacing area, and the size of fracture length relative to the drainage radius. Valko et al. (1997) converted the data in Fig. 12 into the following correlation: 𝑥𝑓 1.65 − 0.328𝑢 + 0.116𝑢2 𝑠𝑓 + ln ( ) = 𝑟𝑤 1 + 0.180𝑢 + 0.064𝑢2 + 0.05𝑢3
2. Calculate the fluid lost in terms of its average width and its volume by: 𝑊𝐹𝐿 = 3𝐶𝑇 0.5
(15)
𝑉𝐹𝐿 = 𝐴(3𝐶𝑇 0.5 )
(16)
3. Select a pad volume which is about 40% of VFL, the fluid lost. 4. Taper proppant in stages ranging from about ¼ up to 10 or 12 pounds of proppant per gallon of liquid (ppg) at the surface. Select stage volumes to achieve sand concentrations in the fracture which begin at about 2 ppg and increase to about 15 ppg. Proppant Scheduling Procedure 1. Select a target productivity increase, fracture length and conductivity that seems desirable and practical
Where, u = ln (FCD).
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2.
3.
4.
5. 6. 7. 8.
for this well by use of McGuire-Sikora Chart. See Figure 19. Select a fluid which provides good fluid loss control, with low spurt loss. Obtain the best available laboratory data for the fluid loss coefficient, C, for the temperature, time exposure, and reservoir characteristics expected during the job. For the frac design multiply the laboratory C factor above by 1.5 to provide 50% safety factor. This step is to allow for some unplanned things which may happen in the field, i.e.: Inadequate product quality Instrument malfunction Equipment failures during the job Careless mistakes made by service or company personnel on location Estimate or calculate an average fracture width using the Geertsma and deKlerk equation with the high viscosity fracture design program by McLeod. Calculate the created fracture area and the fluid lost from equation (1) and (3) Select a pad volume which is 40% of VFL, the fluid lost during the frac job. Select proppant stages with which start at ¼ and increase to 10 to 12 pounds per gallon of liquid. Calculate the final sand concentration and location of the leading and trailing edge of each stage, using McLeod’s program: 𝐶
𝑐𝑓 = 𝑐𝑖 {1 +
√𝑆𝑖 +1
𝑆𝑇𝑂𝑇 −𝑆𝑖 −1
∆𝑉
5.237 √ 𝑊 𝑄
𝑉
(18)
𝑖
𝑆𝑖 = ∆𝑉𝑖 and 𝑆𝑇𝑂𝑇 =
The schedule is generated numerically by iteration. The first iteration starts with an initial schedule with two stages: a small pad stage and a slurry stage of the specified maximum proppant concentration. The schedule is executed using a fracture simulator. Inside the fracture simulator, the schedule is divided into substages with one sub-stage for each time step. The fluid and proppant volumes of each sub-stage are tracked as the sub-stages flow inside the fracture toward the fracture tip. The flow inside the fracture is assumed to be 1D along the fracture length, and the displacement of the sub-stages is assumed to be piston-like. At the end of each time step, the proppant concentration of each sub-stage inside the fracture is examined. If the concentration is higher than the specified maximum concentration, the propant concentration of the sub-stage in the schedule is adjusted so that the concentration in the fracture would be the specified concentration at this time step if the schedule were re-executed.
(17)
}
𝑃
𝑖 𝑐𝑖 = 1+0.045 𝑃
two basic requirements in the conventional PSG conceptual model: one is that the proppant flow front reaches the fracture tip just as the fracture grows to the specified length; the other is that the proppant concentration inside the fracture reaches the specified maximum value along the fracture length at the end of pumping. The proppant concentration may ramp down near the fracture tip.
𝑉𝑇𝑂𝑇 ∆𝑉
=
𝑉𝑃𝐴𝐷 +𝑉𝑇𝑅𝑇.𝐹𝐿+𝑉𝑆𝐴𝑁𝐷 ∆𝑉
(19)
Gu’s Pump Schedule Generator In Gu’s method, a lag-length concept is implemented in a new PSG to control the distance between the proppant flow front and the fracture tip. The lag-length is necessary to prevent premature bridging and screenout in many situations. In this new PSG, the laglength is automatically determined to generate an optimum schedule that uses the minimum pad volume to avoid premature screenout. The PSG is based on a pseudo-3D fracture model, and schedules can be designed for conventional (non-TSO) or TSO treatments. The purpose of a PSG is to automatically generate a pump schedule that includes the amount of fluid in the pad stage and the ramping of proppant concentration in the slurry stages, based on specified fracture length and proppant concentration inside the fracture. There are
III. Simulation In this study, FracCADE 5.1. was used to simulate the hydraulic fracturing treatment which the schedule was exerted from two different methods, which are Crawford’s method and the Gu’s automated method. The data used to be the zone input data in the simulator and also input for Crawford’s method calculation was taken from Rian Rachmanto’s magister thesis, Discrete Fracture Network Model Application, With P3D Model Approach for Hydraulically Induced Fracture in Shale Gas Reservoir. The data was gathered from Rengat Block located in Central Sumatera Basin (CSB), which is a shale formation. This simulation doesn’t do a sensitivity study of using different type of proppant and treatment fluid. The treatment fluid used is YFGOIV, which is an oil based treatment fluid. This fluid is selected as the best fluid that is available in the simulator because of its high viscosity, stability at high temperature, and also the fact that oil is the fluid’s base will only benefit the operation at the shale formation. Then it is safe to say that the fluid’s compatibility to the formation (shale) doesn’t affect the simulation’s result.
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The proppant selected is 20/40 Brady sand because of the fact that sand proppants are currently being widely used and high success ratio to prop the fracture. After comparing the results from both method, a few modifications will be applied to the earlier method based on the several things that can be seen from the later method to be meaningful to lift the productivity index, and the result will be compared to both of the methods. KGD fracture model is selected for all of simulation. The selection of KGD fracture model is based on how the KGD model proved to be useful for understanding fracture growth in the reservoir. In this case, KGD model extends its fracture length on the horizontal axis only (x-axis), while other types of fracture model expand to the vertical axis as well (y-axis). This simplifies the task of finding the breakthrough on what action can be taken to spread the final proppant concentration in the fractured area more evenly. With the usage of KGD model, a few assumptions have to be taken, which are:
Crawford's Method Calculations
Simulation using Schedule Exerted from the Calculation
Simulation using Schedule from Pump Schedule Generator
Analysis of the Results
Simulation using Schedule from Modified Crawford's Method
Comparison Between Three Results
The fracture is propagated in a well-confined pay zone, which means the fracture won’t go through the zone barriers to the respective upper and lower zone. Flow rate in the fracture was constant Pressure in the fracture could be approximated by a constant pressure in the majority of the fracture body
The inputs needed for PSG to be able to run are the desired fracture model, design length, pumping rate, main and flush fluid to be used, round off of the fluid stage, the proppant to be used, first proppant concentration, proppant step size, and maximum proppant concentration in the treatment fluid.
The simulation can be broken down into several stages which can be seen in Figure 13.
Simulation using Schedule Crawford’s Method (Case C)
Crawford’s Method Calculation (Case A)
After both simulations are being run, the results are also being analysed. The analysis is available in the chapter 4, Result and Analysis.
The procedure of Crawford’s method to determine the correct schedule for hydraulic fracturing treatment is written on chapter 2, and was calculated in Microsoft Excel, exerting the volume of treatment fluid and propladen fluid needed, the mass of proppant needed, and ultimately the treatment schedule itself, to yield the desired fractured length. The calculation counting in the created fracture width, fluid lost during fracturing, and also the fold of increase for before and after the treatment operation is run. The calculation and the schedule result can be seen in Figure 20 and 21.
Figure 13 - Simulation and Analysis Flowchart
from
Modified
In short, three changes may be applied to the schedule from the schedule exerted by Crawford’s method, which are adopted from Gu’s PSG method. They are: Not only the proppant concentration, but the fluid volume is also being tapered, and ends with large volume portion on the last prop laden fluid concentration. More proppant mass than before (because of larger volume portion on the last prop laden fluid concentration) Pad fluid volume is timed by 1.5x.
Generating Schedule using Pump Schedule Generator from FracCADE 5.1. (Case B) FracCADE 5.1. provides the Pump Schedule Generator (PSG) to help people easily create a treatment schedule resulting a highly conductive fracture.
IV. Result and Analysis Summary Results of the Three Cases Using FracCADE 5.1., a simulation using the schedule exerted from the calculation using Microsoft Excel that
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can be seen in Figure 20. The results of all three simulations can be seen in figure 23-24, 27-28, and 3132. It can be seen from the figures that all of them resulting a fracture length of more than 500 feet, which is the ideal fracture length for a reservoir with a drainage area of 60 acres (re = 912 ft) based on a reasonable target of fracture length, half of the drainage radius. In term of fracture length, Case A has the best value. Other than that, results from case A have a lot of aspects that is relatively inferior if compared to case B. When it comes to propped fracture width, effective conductivity, effective FCD, and the look of proppant concentration profile across the fracture length, even most of the time case C leads amongst the three cases. Links Between Proppant Concentration Distribution, Fracture Conductivity, and the Schedule After an observation on the results, the schedule exerted by both methods are also being examined. It can be seen from both schedules and the proppant concentration that the proppant concentration distribution correlates heavily and linear to the conductivity of the fracture, because both graphs look almost the same. The pictures of proppant concentration profile and conductivity profile across the fractured area are available in Figure 23-24, 27-28, and 31-32 for each cases. It can be seen from the proppant concentration distribution along the fracture by case A that the proppant is not distributed evenly across the fracture area. The final proppant concentration is diminishing at the tip of the fracture. If the proppant concentration profile of both results of case A and case B are compared, the maximum conductivity region in the fracture area exerted by case A (1586 - 1928 md.ft) only exist until about 225 ft from the wellbore, while the same value of conductivity can be found in the result exerted by Case B at about 500 ft from the wellbore. This is the main aspect that is seen as the most critical difference between both methods.
earlier stage of pumping (low concentration fluid) takes the place nearer to the fracture tip, and the later stage of pumping (high concentration fluid) takes the place nearer to the wellbore. The assumption explains why case A’s schedule exerted a fracture with proppant concentration distribution as can be seen in Figure 2324. Based on that assumption only, all of the results and the schedule exerted by each cases are somewhat linked. The improved version (case C) adopts PSG’s approach that the concentration at early times is designed to be acceptably low to prevent proppant bridging from excessive proppant concentration near tip fracture (lag length), then exponentially improved, which gives large volume proportion at the max concentration prop laden fluid. This brings one drawback that can be seen from case B’s schedule, we need more proppant mass (1.5x case A’s total mass) to frack the same fracture length. But with that drawback, the effective conductivity across the fracture is nearly doubled. There is a study which learns the advantages of having more proppant concentration in the fracture area. There are three highlighted benefits that can be gained by having greater proppant concentration in the fracture area: Wider Fracture Width The study explains the correlation of sand concentration with fracture. It can be seen that both correlates linearly, which means higher sand concentration will only gain larger fracture width value. The results of simulations are also showing the same correlation between sand concentration and fracture width. Case C exhibit the highest average proppant concentration in the fracture area, and case C also exerts the highest average fracture width along the fracture.
It can be seen also that the schedule’s characteristics determines the proppant concentration distribution in the fracture area. In case A’s schedule, each different stages (1.0 PPA, 2.0 PPA, etc) has the same volume of prop laden fluid, while in case B the higher proppant concentration stages are being pumped faster that case A. Case B only need about 1400 gallon of 1.0 and 5.0 PPA stages before it enters the 8.0 PPA stages. The rest of the operation runs with prop laden fluid with at least 9.0 pounds of proppant added. These two distinct characteristics of schedule can be correlated directly to the results by assuming that the
Figure 14 - The relation between sand concentration with the created fracture width (Coulter et. al, 1972)
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Lower Portion of Sand Crushed This phenomena of sand crushing by the closure pressure in the fracture area is actually depends on the proppant strength. The type of proppant that is used in the study is also Brady sand, which is not too strong in higher closure pressure.
Higher Flow Capacity The result of the study indicates that for the concentration evaluated the fracture flow capacity increases as the sand concentration increases.
Figure 15 - Relation between sand concentration and portion of sand crushed (Coulter et. al, 1972)
If the proppant concentration is quite small, a partial monolayer proppant arrangement can be found in the fracture area. Thus, if the proppant is not crushed, an embedment phenomenon can be found, which also decreases the conductivity of the fracture. And if it’s crushed, it’s said that the crushing will be more severe in the lower concentration than in higher concentration. Higher proppant concentration will only benefit the operator in higher conductivity value, because multilayer proppant arrangement will be met, and the fracture area will behave as if it is a sand reservoir.
Figure 17 - Relation between sand concentration and fracture flow capacity (Coulter et. al, 1972)
Difference in Pad Fluid Volume From Figure 21 and 25, it can be observed that the total pad fluid volume from case A is about 1800 gallon, and from case B is about 2900 gallon. From the definition of pad stage, the fluid volume injected will correlates to the fracture length created by the pad stage. Instead of following that definition, the results of the simulation are different. The fracture length created by the case B is slightly lower than the case A’s. Firstly, case C was also run with 1800 gallon of pad fluid volume, just like case A. But then it turns out that the fracture created was only 320 ft long (roughly 65% of case A’s). This phenomenon is caused by the increasing value of fracture width in case C, which also lift the volume of pad fluid needed to open the fracture in the first place. With the same fracture length and 1.5 times more fracture width, the volume of pad fluid needed would also be 1.5 times more than before. So after this analysis, case C’s pad fluid volume was altered to be 1.5 times higher than before. Then the results show the fracture length is considered to be in the region of acceptance (± 500 ft) with a lifted value of fracture width. Results of the Modified Crawford’s Method (Case C)
Figure 16 - Proppant arrangement in the fracture area (Schechter, 1992)
As what has been analysed and can be seen in Figure 33, results of case C has better values in the most of parameters except the fracture length and fluid efficiency, which case A’s result has better values, and the last segment’s conductivity (near the tip of fracture), which is lost only to case B’s result. The case C simulation result which shows the fracture conductivity and proppant concentration distribution in
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the fracture can be seen in Figure 31-32. The result also shows that the created fracture has a better proppant concentration distribution than the case A. To compare it with an apple-to-apple comparison, the created fracture which has the conductivity in the region of 1586 md.ft and larger takes place roughly 0-450 ft from the wellbore (case A = 0-225 ft, case B = 0-500 ft). This value shows that case C has a better proppant concentration distribution, thus also better overall fracture conductivity than case A. Although case B still has the better distribution than case C, case C’s result still has the better effective fracture conductivity through all the fracture area. According to Schechter, R.S. in his book, the stimulation ratio from fracturing treatment in gas well cannot be correctly predicted by McGuire-Sikora chart. The chart is developed by assuming that the flow into the wellbore of the unstimulated well follows Darcy’s law and that the flow of fluid through the fracture into the wellbore is laminar. Both of these assumptions may be incorrect when applied to gas wells. The corrections for turbulence are generally best handled using a reservoir simulator so that the nonlinear, turbulent flow behaviour can be accurately predicted.
V. Conclusion and Recommendation Conclusion 1. Quality comparison between all cases: Proppant concentration distribution, case B is a remarkable upgrade for case A. Total Proppant Mass, case B uses 1.5x more proppant than case A. Pad fluid volume, case B uses 1.5x more pad fluid than case A. Schedule, the schedule exerted by case B doesn’t need to pump the low concentration slurry for a long time. Low concentration slurry is only needed to give the lag length needed. Thus, case B’s fracture result is dominated by large proppant concentration, which makes case B having the best conductivity distribution along the fracture. 2. Comparison of the results between each method can be seen in Figure 33. In summary, here are few parameters with each method with the best value:
Fracture Half-Length: Case A Fracture Width: Case C Fluid Efficiency: Case A Effective Conductivity: Case C Effective FCD: Case C Maximum Surface Pressure: Case C
Average Proppant Concentration: Case C Maximum Proppant Concentration: Case C Last Segment’s Conductivity: Case B Recommendation 1. This study has to be confirmed with another try in different formation. 2. Try to apply graded proppant size in a schedule to maximize conductivity in the near fracture tip area.
VI. Acknowledgment There are a few parties that has helped the writer to complete this study and also to complete this study. Firstly, the writer wants to thank God for all of His blessings that writer has received until this very moment. Secondly, writer also want to thank these following parties: 1. Prof. Dr. Ir. Sudjati Rachmat, DEA and Wijoyo Niti Daton, S.T., M.T., as writer’s dearest lecturers for their kindness and patience to guide writer to write a good thesis. 2. Writer’s family, who do not stop encouraging and inspiring writer to strive to do the best in each and every moment. 3. Writer’s friends, Evans Immanuel, Franky Octavius, Andreas Ansen, Ryan Kurniawan Santoso, M. Ansy Alghasi, M. Iffan Hannanu, Rizky Primayudha, who have helped writer in building the content of this study. 4. Writer’s batch in Petroleum Engineering ITB 2012 - Petroverso, for the moments writer has spent and made the writer who he is. 5. All other parties who have helped the writer directly or indirectly.
VII. References Cipolla, C. L., “Modeling Production and Evaluting Fracture Performance in Unconventional Gas Reservoirs”, Journal of Petroleum Technology, 2009. Coulter, G. R., and Wells, R. D., “The Advantages of High Proppant Concentration in Fracture Stimulation”, Journal of Petroleum Technology, SPE3298, 1972 Crawford, H. R.: “Proppant Scheduling and Calculation of Fluid Lost”, SPE-12064, 1983.
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Economides, M., Oligney, R., and Valkó, P., “Unified Fracture Design”, Texas: Orsa Press, 2002. Gu, H., and Desroches, J.: “New Pump Schedule Generator for Hydraulic Fracturing Treatment Design”, SPE-81152, 2003. Guo, B., Ghalambor, A., and Lyons, W. C.: “Petroleum Production Engineering: A ComputerAssisted Approach”, Lafayette: Elsevier Science & Technology Books, 2007. Hidayat, R., Maulana, J., Asnanda, G., and Kukuh, K., “Peningkatan Produksi Minyak Melalui Hydraulic Fracturing di Struktur Cemara”
McLeod, H. O., “A Simplified Approach to Design of Fracturing Treatments Using High Viscosity CrossLinked Fluids”, SPE/DOE-11614, 1983. Nolte, K. G.: “Determination of Proppant and Fluid Schedules from Fracturing-Pressure Decline”, SPE18357, 1986. Rachmanto, R., “Discrete Fracture Network Model Application with P3D Model Approach for Hydraulically Induced Discrete Fractures in Shale Gas Reservoir”, Bandung: Institut Teknologi Bandung, 2012. Schechter, R. S.: “Oil Well Stimulation”, New Jersey: Prentice Hall, 1992.
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Figure 18 - Different type of proppant and their permeability in different closure stress
Figure 19 - McGuire-Sikora chart for determining fold of production increase after a fracturing treatment (McGuire-Sikora, 1960)
Figure 20 - Calculation process in determining hydraulic fracturing treatment schedule by Crawford's method
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Figure 21 - Case A (Crawford's method) schedule
Figure 22 - Summary results of case A
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Figure 23 - Case A's proppant concentration and conductivity in the fractured area
Figure 24 - Case A's proppant concentration and conductivity contour in the fractured area
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Figure 25 - Case B (Pump Schedule Generator) schedule
Figure 26 - Summary results of case B
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Figure 27 - Case B's proppant concentration and conductivity in the fractured area
Figure 28 - Case B's proppant concentration and conductivity contour in the fractured area
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Figure 29 - Case C's (Modified Crawford's method) schedule
Figure 30 - Summary results of case C
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Figure 31 - Case C's proppant concentration and conductivity in the fractured area
Figure 32 - Case C's proppant concentration and conductivity contour in the fractured area
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Figure 33 - Comparison between summary results of the three cases
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