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`SPE 125526
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`Horizontal Well Completion, Stimulation Optimization, And Risk Mitigation
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`Larry K. Britt, NSI Fracturing, LLC and Michael B. Smith, NSI Technologies, Inc.
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`Copyright 2009. Society of Petroleum Engineers
`
`This paper was prepared for presentation at the 2009 SPE Eastern Regional Meeting held in Chaneston, West \firginia, USA, 23—25 September2009
`This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents 01 the paper have not been
`reviewed by the Society 01 Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers. its
`officers. or members. Electronic reproduction, distribution. or storage 01 any part oi this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to
`reproduce in print is restricted to an abslract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
`
`Abstract
`
`Horizontal wells have become the industry standard for unconventional and tight formation gas reservoirs. Because these
`reservoirs have poorer quality pay, it takes a good, well-planned completion and fracture stimulation(s) to make an economic
`well. Even in a sweet spot in the unconventional and tight gas reservoir, good completion and stimulation practices are
`required; otherwise, a marginal or uneconomic well will result. But what are good completion and stimulation practices in
`horizontal wells? What are the objectives of horizontal wells and how do we relate the completion and stimulation(s) to
`achieving these goals? How many completions/stimulations do we need for best well performance and/or economics? How
`do we maximize the value from horizontal wells? When should a horizontal well be drilled longitudinally or transverse?
`These are just a few questions to be addressed in the subsequent paragraphs.
`
`This paper focuses on some of the key elements of well completions and stimulation practices as they apply to horizontal
`wells. Optimization studies will be shown and used to highlight the importance of lateral length, number of fractures, inter-
`fracture distance, fracture half-length, and fracture conductivity. These results will be used to discuss the various completion
`choices such as cased and cemented, open hole with external casing packers, and open hole “pump and pray” techniques.
`This paper will also address key risks to horizontal wells and develop risk mitigation strategies so that project economics can
`be maximized. In addition, a field case study will be shown to illustrate the application of these design, optimization, and risk
`mitigation strategies for horizontal wells in tight and unconventional gas reservoirs.
`
`This work provides insight for the completion and stimulation design engineers by:
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`1.
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`2.
`9:
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`4.
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`developing well performance and economic objectives for horizontal wells and highlighting the incremental benefits
`of various completion and stimulation strategies,
`establishing well performance and economic based criteria for drilling longitudinal or transverse horizontal wells,
`integrating the reservoir objectives and geomechanic limitations into a horizontal well completion and stimulation
`strategy, and
`identifying horizontal well completion and stimulation risks and risk mitigation strategies for pre-horizontal well
`planning purposes.
`
`Introduction
`
`For many years, operators have utilized hydraulic fracturing to improve the performance of vertical, deviated, and
`horizontal wells. Although often successful, these operators have reported more difficulty fracture stimulating deviated and
`horizontal wells than that which occurred during the stimulation of vertical wells in the area. Generally, the difficulties of
`fracture stimulating deviated and horizontal wells are evidenced by increased treating pressures and elevated post-fracture
`Instantaneous Shut-In Pressures.
`
`Horizontal wells have been successfully applied in a number of field applications over the years. Recent applications in
`the Barnett Shale Formation in the Fort Worth Basin have raised attention to the application of this technology to Tight
`Formation and Unconventional Gas Resources. Though the application of horizontal well completion and stimulation
`technology has been successful, the completion and stimulation technology applied in each varies widely. It is the objective
`of this evaluation to develop an understanding of each of these “completion and stimulation styles.” Through this
`understanding, reservoir, completion, and stimulation criteria will be developed to aid in identifying which strategy, if any, to
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`apply in a given asset to maximize the production rate, reserve recovery, and economics.
`Horizontal wells have been shown to improve well performance in oil and gas reservoirs especially when coupled with
`hydraulic fracturing”. Completions for multiple fractured horizontal wells have been a constant issue since the technology
`became popular in the early 1990’s. In the North Sea, several methods of perforating, stimulating, and isolating have been
`utilized to improve well completion efficiency and fracture stimulation pluCClnCI'llR-IZ. Although effective, these completion
`techniques struggled to find an on—shore commercial market
`in Light and unconventional gas reservoirsn‘lé where more
`completions and fractures are desired per foot of lateral length.
`In tight and unconventional gas reservoirs, greater operational control and reliability are necessary for operational success
`and to prevent erosion of project economics. Numerous papers have described the problems associated with open hole or
`slotted liner completions where limited to no control of the injection fluids is availablel7'lg. In these works, Inieroseistnic
`and/or tiltmeters were used to show that
`in an uncemented slotted liner completion”,
`the resulting fractures Were
`concentrated at the heel and toe of the well with no effective stimulation seen through most of the lateral. In one paper‘s,
`tiltmeters showed that a transverse fracture was created at the toe of the lateral and a longitudinal fracture created at the heel.
`In another integrated study'g, post-fracture diagnostics confirmed that fractures rarely distributed themselves over the entire
`length of the horizontal section. Depending on hoop stress, fracture initiation may occur at the heel or tow of the lateral, but
`without positive isolation there is no real control over the location or number of fractures generated. Perhaps more
`importantly, there is no control over the stimulation fluid and the resulting dimensions of the created fractures. In these low
`permeability formations, zonal isolation has been shown to be critical to multiple fractured horizontal well successzo'zz. In the
`Barnett Shale Formation, for example, pump llUWI‘I plugs!"24 and external casing packers”26 have been utilized to improve
`isolation and improved fracture stimulations have been the result. The pump down plug system is used in cased and cemented
`horizontal well applications and allows nearly complete control over the injected fluids. The external packer system, although
`an openhole application, does allow the design engineer to exert some control over the fracture stimulation(s), especially
`when compared to the “pump and pray” completion style (i.e, fully open hole or uncemented slotted liner completions).
`This paper will review multiple fractured horizontal well objectives for tight and unconventional gas reservoirs.
`Geomechanical influences such as principal stresses, hoop stress, and fracture interference will be addressed in the context of
`horizontal well objectives in these reservoirs. This paper will show that it is these geomechanical influences, coupled with the
`horizontal well objectives, that should drive the selection and implementation of a completion system. Further, reservoir,
`completion, and stimulation risks and risk mitigation strategies will be discussed and a tight gas case study shown to detail
`and document the real world implications of the theoretical problems addressed.
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`Discussion
`
`Table 1: Base case Reservoir 8. Economic Parameters
`
`Reservoir Parameters:
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`Horizontal Well Objectives:
`The objective of horizontal wells in tight formation and unconventional gas reservoirs is to improve the gas production
`rate, rate of recovery, and project economics, just as in vertical wells. However, the completion and well stimulation(s) in
`horizontal wells are far more complex. The role of this section is to establish a framework for developing the horizontal well
`objectives. The best way to do that is with a reservoir simulator
`and economic model. Through the integration of this data, the
`critical objectives for horizontal well success can be determined.
`The subsequent paragraphs will detail and document an analysis
`of reservoir,
`fracturing, and economic parameters and their
`importance inr maximizing horizontal well economics. The
`simulator used in this analysis is the numeric three-dimensional
`single phase gas simulator in STIMPLAN. The simulator has an
`automated horizontal well gridding feature, and it has been used
`for horizontal well studies for nearly two decades.
`The base case reservoir and economic parameters used in this
`study are shown in Table 1. These base case parameters are
`fairly typical of tight formation gas reservoirs in the United
`States. However, numerous sensitivity tests were conducted to
`ensure that the assumptions made and used in this economic
`study were reasonable and didn’t unduly influence the results.
`First, let’s look at the effect of lateral length on horizontal
`well performance. Figure 1 shows a plot of Net Present Value
`versus the Number of Fractures as a function of Lateral Length
`for the base case parameters from Table 1. As shown, with one
`fracture in the horizontal well in a tight gas reservoir, there is
`the benefits of
`marginal economic benefit of increased lateral
`length. However, as the number of fractures increases,
`increasing lateral length increases as well. For example, for the case where 15 completions/fractures are created, the net
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`Figure 1: Economic Effect of Lateral Length
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`present values for the 1,000 ft, 2,000 ft, 3,000 ft, and 4,000 ft lateral are 8.8 M$, 15.1 M$, 20.6 M$, and 25.1 M$,
`respectively. Note, that this benefit is realized regardless of the——
`natural gas price. It is sensitive to the cost of drilling the lateral,
`however, but even then the cost of extending the lateral would
`need to increase by 16.5 times (i.e, from $400/ft to $6,600/ft) for
`the economic benefits of increased lateral
`length to be fully
`eroded.
`
`Also shown on this plot are the economic values of a 2,000
`foot longitudinal and 3,000 foot longitudinal horizontal well. As
`shown, the values of these longitudinal horizontal wells are 2.7
`M$ and 4.9 M$, respectively. Thus, the net present value of a
`longitudinal well in a tight gas and unconventional reservoir is
`far less than that of a multiple fractured transverse well.
`Next, let’s look at the effect of fracture length on horizontal
`well economic performance. A 3,000 foot lateral was considered
`with fracture half-length varying from 500 to 2,000 feet, as
`shown in Figure 2. The economic benefits clearly increase as the
`fracture half-length increases. For example, for the case where
`15 completions/fractures are created the net present value for the
`500 ft, 1,000 ft, 1,500 ft, and 2,000 ft fracture half-length is 7.7
`M$, 14.6 M$, 20.6 M$, and 25.6 M$, respectively. Note that
`economic benefit of increased half-length is realized regardless
`of the natural gas price. Much like the benefit of increased lateral
`length, that of increased half-length is sensitive to the fracturing
`costs; however,
`it would require the costs per square foot of
`fracture to increase by 108 times (i.e, from $1.2/ft2 to $130.0/ft2)
`for the economic benefits of increased fracture length to be fully
`eroded.
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`Figure 2: Economic Effect of Fracture Length
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`Figure 3: Optimum Completion Spacing versus Permeability
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`
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`In this analysis we have looked at the economics of various
`parameters as a function of the number of completions/fractures. Figures 1 and 2 distinctly show that there is an economic
`benefit from increasing the number of completions/fractures, but clearly there are diminishing returns. This can be best seen
`by reviewing either the 1,000 foot lateral case in Figure l or the 500 foot fracture half-length case in Figure 2. In either
`example, when the number of completions/fractures exceeds 8 to 10 no additional economic benefit is realized. Of course, as
`the lateral length and fracture half-length increases, the number of completions/fractures from which an economic benefit is
`derived increases as well. Further, this optimum number of completions/fractures is a function of reservoir permeability. To
`investigate this further, an optimization of the number of completions/fractures was conducted using the base case properties
`and varying reservoir permeability. This optimization is shown in Figure 3, a plot of the optimal distance between
`completions/fractures as a function of the reservoir permeability. This figure represents the result of hundreds of simulations,
`as displayed in Figures 1 and 2, and provides an interesting
`horizontal well design objective, whether in an unconventional
`shale gas, tight formation gas, or conventional gas reservoir. As
`shown, for a reservoir permeability of 0.0001 md the optimal
`distance between completions/fractures is slightly over 100 feet,
`while for reservoir perrneabilities of 0.01 and 0.1 md the optimal
`distances between completions and fractures are nearly 500 and
`1,000 feet, respectively. The higher the permeability, the greater
`the optimal distance between completions and fractures is. This
`indicates
`that
`the
`economic driver
`for multiple
`fractured
`horizontal wells is the communication or interference of the
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`created fractures, and this communication is largely driven by
`the matrix permeability of the reservoir. Although not the subject
`of this paper, this raises an interesting question regarding the
`economic value of a naturally fissured medium, especially when
`the fissures require injected fluids to activate.
`In this section, we showed the key economic drivers of horizontal wells which are the lateral length and fracture half
`length. Of the two, fracture half-length is the most important based on the net present value contribution per foot; however,
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`we do not have total control over how long a fracture we are able to create. As a result, a critical part of establishing
`horizontal well objectives is to understand the basis of fracture design (i.e, in-situ stress, Young’s Modulus, and leak-off) so
`that a reasonable economic projection can be made.
`
`As one final thought, we showed the benefits of fracture length and lateral length on the horizontal well economics. Other
`parameters such as fracture conductivity, net pay, and reservoir pressure were investigated. Their effects on the horizontal
`well economics were found to be fairly predictable and not nearly as important to the completion process as length (i.e, either
`lateral or fracture). However, fracture conductivity was found to be important for the case where non-Darcy convergent flow
`was deemed important. As such, the effect of fracture conductivity on horizontal well performance will be discussed in a
`subsequent section on horizontal well risk mitigation strategies.
`
`Geomecham'cs ofHorizontal Well Completions:
`Why do fracture stimulations in deviated and horizontal wells differ from fracture behavior in vertical wells? To
`understand this difference, we need to consider rock mechanics and more specifically the state of stress and how it impacts
`the hoop stresses around the borehole. In a vertical well, the principal stresses are rectangular and they include a vertical
`stress, ov, maximum horizontal stress, onax, and minimum horizontal stress, ohm. Figure 4 shows a schematic of the various
`stress states (stress environments) and the relationship of the
`principal stresses for normal, Strike—Slip, and Reverse/Thrust
`fault environments
`
`Figure 4: Schematic of Conventional Stress States
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`In a normal stress environment, a fracture opens against the
`minimum horizontal stress (fracture opening/closure pressure)
`and propagates in the direction of the maximum horizontal stress
`(perpendicular
`to the minimum horizontal
`stress).
`In this
`environment, the induced stress concentrations or hoop stresses
`are maximized (breakdown pressures
`are high) when the
`minimum and maximum horizontal stresses are equal or nearly
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`so. When the max1mum to minlmum horizontal stress ratlo 1s
`large (>>>1), the hoop stresses are small and the breakdown
`pressure is minimized. Figure 4 shows this state of stress in
`rectangular coordinates. It should be noted that in deviated wells,
`the principal stresses are similar except that they are expressed in
`radial coordinates. This is shown in Figure 5, which is a
`schematic of a deviated wellbore that has a relation to the
`
`rectangular coordinates of (TV, onax, and em“. In addition, the
`well deviation, 0, the well azimuth (deviation from maximum
`horizontal stress), 0t, and where on the borehole the breakdown
`occurs,
`42, displays
`the tangential
`stresses associated with
`deviated wellbores. The works of Bradley27 and Deily &
`Owens28 were used to translate the equations for the rectangular
`stress state to the radial stress state, and a program based on
`these equations was developed. This was used to assess the
`breakdown pressure as
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`a function of B, 09 and 4), assuming the ”normal” stress state
`where the overburden is the maximum principal stress,
`the
`maximum horizontal stress is the intermediate principal stress,
`and the minimum horizontal stress is the minimum principal
`stress. Assuming that the overburden stress is l psi/ft (10,000 psi
`for a 10,000 foot vertical well), the intermediate and minimum
`principal stresses are 7,500 and 6,000 psi,
`respectively,
`the
`reservoir is normally pressured (4,300 psi), the tensile stress is
`300 psi, and Poisson’s Ratio is 0.20, the breakdown pressure for
`horizontal wells with azimuths of 0 (longitudinal), 30, 60, and 90 (transverse) degrees are 4,000, 4,100, 5,980, and 8,500 psi,
`respectively. Thus, the breakdown pressure for a horizontal well aligned with the minimum horizontal stress (onax >>>
`ohmin) is more than two times the breakdown pressure for a horizontal well aligned with the intermediate stress. Figure 6
`shows a plot of breakdown pressure versus theta (location on the wellbore) for varied well azimuths. As shown, for any
`azimuth, the lowest breakdown pressure occurs at a theta of 0 degrees which indicates that the horizontal well, regardless of
`azimuth, will breakdown at the top and bottom of the wellbore. Further, the sides of the wellbore have breakdown pressures
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`Figure 6: Wellbore Breakdown Pressures (O'Hmax >>> O'hmin)
`
`nearly five times that of the top and bottom. For this particular example, the breakdown pressure for the side of the wellbore
`is nearly 20,000 psi for the longitudinal case and 18,000 psi for the transverse horizontal well case. For open hole
`completions and stimulations, the distinction of where on the wellbore breakdown occurs is irrelevant. However, for cased
`and cemented wells, this distinction is quite important. What if no consideration is given to the perforation strategy in a cased
`and cemented wellbore? What if the perforations are 30 degrees from the top of the wellbore (theta is 30 degrees)? For the
`assumptions used in this example, that scenario would result in wellbore breakdown pressures of 8,000 and 11,000 psi for the
`longitudinal and transverse horizontal well cases, respectively. Thus, the lack of a perforation strategy in a cased and
`cemented horizontal well can easily result in breakdown pressures
`two to three times that of an open hole horizontal wellbore. When
`you hear of a cased and cemented wellbore that couldn’t be broken
`down, ask yourself, what perforation strategy was used?
`Next,
`let’s review a “normal” stress condition where the
`maximum and minimum horizontal stresses are nearly 1. That is, a
`stress state where the maximum horizontal stress is the weight of
`the overburden and the intermediate and minimum horizontal
`
`the
`stresses are nearly equal. For this example, assume that
`overburden stress is again 10,000 psi but
`the minimum and
`maximum horizontal
`stresses
`are
`7,500
`and
`7,300
`psi,
`respectively. Figure 7 shows a plot of the wellbore pressure versus
`theta as a function of azimuth for a horizontal well. As shown, the
`breakdown pressure (where the wellbore pressure is the lowest)
`occurs at the top and bottom of the wellbore regardless of the well
`azimuth. Further, when the wellbore is aligned with the maximum
`horizontal stress (azimuth is 0 degrees), the wellbore breakdown
`pressure is 7,900 psi. When the azimuth of the wellbore is 90
`degrees (transverse) the wellbore breakdown pressure is 8,500 psi.
`Thus, when the horizontal stresses are equal or nearly so,
`the
`difference between the breakdown pressures of an aligned or
`longitudinal wellbore and a non-aligned or transverse wellbore is
`minimal (i.e. 600 psi). Compare this to the prior case where the
`maximum to minimum horizontal stress ratio was much greater
`than i and the difference in breakdown pressure between an
`aligned (longitudinal) and unaligned (transverse) wellbore was
`4,500 psi. Such a difference in breakdown pressure can be readily
`appreciated if you realize that when the maximum to minimum
`horizontal stress ratio is greater than 1 (onax>>> ohmin) there is a
`preferred fracture direction, and a potentially large penalty is
`realized when the wellbore is misaligned with that preferred
`direction. On the other hand, when there is no preferred fracture
`direction (onax~ ohmin), from a breakdown perspective it doesn’t
`particularly matter which direction the well is drilled in.
`Also note by referencing Figure 7 that even when there is no
`preferred fracture direction (onax~ ohmin),
`there is still a strong
`preference for the horizontal well
`to breakdown on the top and
`bottom of the wellbore. Irrespective of azimuth, if a horizontal well
`is cased, cemented, and perforated on the sides of the wellbore, the
`breakdown pressures can exceed 18,000 psi for the example cited
`(i.e. nearly 2.1 times the breakdown pressure for the cased and
`cemented wellbore with the top and bottom perforated).
`What about a Strike-Slip stress environment where the vertical
`stress (overburden) is the intermediate principal stress and the
`maximum horizontal stress
`is
`the maximum principal
`stress?
`Assume that the intermediate stress (overburden) is 7,500 psi for a
`10,000 foot vertical well and the maximum and minimum principal
`stresses are 10,000 and 6,000 psi,
`respectively.
`In addition,
`assuming the reservoir is normally pressured (4,300 psi), the tensile
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`Figure 9: Wellbore Breakdown Pressures (O‘Hmax = cnmin)
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`stress is 300 psi, and Poisson’s Ratio is 0.20, the breakdown pressures for horizontal wells with azimuths ofO (longitudinal),
`
`30, 60, and 90 (transverse) degrees are 6,500, 6,980, 6,960, and
`8,500 psi,
`respectively. Thus,
`the breakdown pressure for a
`horizontal well aligned with the minimum horizontal stress in a
`Strike—Slip environment (6H,nax > 5,) is more than 1.3 times the
`breakdown pressure for a horizontal well aligned with the maximum
`principal and horizontal stress. Figure 8 shows a plot of breakdown
`pressure versus theta (location on the wellbore) for varied well
`azimuths. As shown, the lowest breakdown pressure for azimuths
`of 0 and 30 degrees occurs at a theta of 0 degrees which indicates
`that for this scenario the well will breakdown at the top and bottom
`of the wellbore. Further, for azimuths of 60 and 90 degrees, the
`wellbore has breakdown pressures nearly 1.07 and 1.30 times that of
`the borehole aligned with a 0 degree azimuth.
`If we assume that
`this is a cased and cemented wellbore, we can once again see that
`the perforation strategy is extremely important. For a longitudinal
`horizontal well perforated at the top and bottom of the wellbore, the
`breakdown pressure would be nearly 6,000 psi
`less than for the
`wellbore perforated on its sides. Conversely,
`for a transverse
`horizontal wellbore in a Strike-Slip stress environment, perforating
`on the sides of the borehole results in nearly a 10,000 psi reduction
`in the breakdown pressure compared to perforating on the top and
`bottom ofthe borehole.
`What about a “reverse” or “thrust” fault environment where the
`overburden is the minimum principal stress and the maximum and
`minimum horizontal stresses are the maximum and intermediate
`principal stresses, respectively? To look at the effect of breakdown
`pressures in horizontal wells in a “thrust” environment, let’s assume
`that the overburden pressure is 6,000 psi, the maximum horizontal
`stress is 10,000 psi, and the minimum horizontal stress is 7,500 psi.
`Assume reservoir pressure, tensile pressure, and Poisson’s Ratio are
`as in the prior examples. Figure 9 shows the results of this analysis
`as a plot of Wellbore Pressure as a function of theta for various
`values of azimuth from 0 degrees (longitudinal) to 90 degrees
`(transverse). As
`shown,
`for
`all
`“reverse
`or
`thrust”
`stress
`environment cases, the wellbore breakdown occurs on the sides of
`the horizontal well (theta is 90 degrees). Further,
`in this stress
`environment,
`the minimum breakdown pressure occurs
`in the
`transverse horizontal case and the maximum breakdown pressure
`occurs in the longitudinal direction.
`In this stress environment, the
`breakdown pressure for a 0, 30, 60, or 90 degree azimuth would be
`6,500, 5,660, 4,280, and 4,000 psi, respectively. Finally,
`if you
`cased and cemented the wellbore and perforated the top and bottom
`of the borehole, the breakdown pressure for a 0, 30, 60, or 90 degree
`azimuth would be 20,000, 17,260, 13,620,
`and 12,500 psi,
`respectively. Put differently, a cased, cemented, and perforated
`horizontal well in a reverse or thrust stress environment would be
`difficult if not impossible to breakdown and is, therefore, a poor
`completion choice for this stress environment.
`The preceding analysis of breakdown pressures as a function
`of stress environment highlights how critical it is to understand
`the state of stress prior to selecting a completion and stimulation methodology. Figures 10 and 11 put this analysis in graphic
`form as plots of breakdown pressure versus theta for each stress environment and longitudinal (azimuth is 0 degrees) and
`transverse (azimuth is 90 degrees) cases, respectively. As shown, for longitudinal horizontal wells, the breakdown pressure is
`lowest for a normal stress environment where the overburden, maximum horizontal, and minimum horizontal stress are the
`maximum, intermediate, and minimum principal stresses, respectively. In a cased and cemented wellbore with this stress
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`environment, perforate the top and bottom of the borehole (theta is 0 and 180 degrees). For this example, the breakdown
`pressure in the Strike-Slip or Reverse/Thrust is equal and 2,500 psi higher than the normal stress environment. Note,
`however, that the location where the breakdown occurs varies from the top and bottom of the well (Strike-Slip) to the sides
`of the wellbore (Reverse/Thrust). As a result, a perforation strategy is necessary anytime you case, cement, and perforate a
`horizontal wellbore.
`
`Figure 1 1 shows a similar plot for a transverse horizontal well. As shown, for a transverse horizontal well, the breakdown
`pressure is lowest for a reverse or thrust stress environment where the maximum horizontal, minimum horizontal, and
`overburden stress are the maximum, intermediate, and minimum principal stresses, respectively. In a cased and cemented
`wellbore with this stress environment, perforate the sides of the borehole (theta is 90 and 270 degrees). For this example, the
`breakdown pressure in the Normal or Strike-Slip is equal and 2,500 psi higher than the reverse or thrust stress environment.
`Note, however, that the location where the breakdown occurs varies from the top and bottom of the well (Normal) to the
`sides of the wellbore (Strike-Slip). As a result, a perforation strategy is necessary anytime you case, cement, and perforate a
`horizontal wellbore.
`
`Fracture Interference:
`
`As indicated in the horizontal well objectives section, an attractive option for some low permeability formations is
`multiple, transverse propped fracture stimulations along the length of a horizontal wellbore (as pictured in Figure 12).
`However, as the fractures get closer and closer along the length of the wellbore, they will begin to mechanically interfere
`with one another. For a treatment aimed at creating multiple, transverse fractures, this interference may establish an absolute
`maximum number of fractures that can be created simul-
`
`
`
`Figure 12: MUMPle Fracmred TranSVerse Horizontal we”
`
`taneously. The potential interference is calculated below for the
`case of long, confined height fractures.
`The analysis discussed here was conducted using a finite
`element program, SAP_IV. Along with the results presented
`here, other simulations were conducted using varying grid
`patterns to ensure that the grid was sufficiently fine for accurate
`results. Two separate cases were considered: 1) the case of two
`fractures, and 2) a case of an infinite series of parallel fractures.
`Clearly, any real case (as pictured in Figure 12) would consist of
`both types of cases. That is, for the case in Figure 12, the two
`end fractures would approximately behave like the “2 fracture”
`case below, while the center
`fracture would approximately
`behave like the “N fracture” case. These cases considered two
`
`long, confined height fractures running parallel to one another
`along their length (as pictured in the inset of the figures below).
`Figure 13 plots the results for two parallel fractures. First, the width reduction is plotted as a function of dX/H (where dX is
`the distance between fractures and “H” is the fracture height). This shows that for dX/H=l, the width of each fracture is
`about 80% of the width of a single fracture (for the same fluid pressure). However, the total width is greater since there are
`now two fractures!
`
`This is seen in the “Flow Resistance”. For a viscosity dominated fracture behavior, the net pressure at the wellbore is
`given (approximately) by
`
`1/4
`
`E Q L
`
`PM ocfi(——g]
`
`or
`
`.
`
`PNE, oc E 3/4 X Q1/4 I
`
`Thus, for the case of dX/H:l, the width for each of two fractures is 0.8 X W0, i.e., where W0 is the width for a single
`fracture. This is equivalent to a modulus increase by a factor of 1.25 (i.e., 1/0.80). However, the flow rate is now cut by 50%
`since there are two fractures. Thus, the “flow resistance” is given by
`
`E' 3/4 x Q'” = (1.25)“ x (0.5)”4 = 0.995
`
`That is, the “flow resistance” for two parallel fractures with a spacing of dX/H=1 is identical to the flow resistance for a
`single fracture. Fo