Methodology to Predict the Initiation of
`Multiple Transverse Fractures from
`Horizontal Wellbores
`
`D.G. CROSBY, Z. YANG, S.S. RAHMAN
`University of New South Wales
`
`Abstract
`Multi-stage, transversely fractured horizontal wellbores have
`the potential to greatly increase production from low permeabili-
`ty formations. Such completions are, however, susceptible to
`problems associated with near-wellbore tortuosity, particularly
`multiple fracturing from the same perforated interval. A criteri-
`on, based on that by Drucker and Prager, has been derived,
`which predicts the wellbore pressures required to initiate sec-
`ondary multiple transverse hydraulic fractures in close proximity
`to primary fractures. Secondary fracture initiation pressures pre-
`dicted by this new criterion compare reasonably well with those
`measured during a series of unique laboratory-scale multiple
`hydraulic fracture interaction tests. Both the multiple fracture
`initiation criterion and the laboratory results suggest that close
`proximity of primary hydraulic fractures increases the initiation
`pressures of secondary multiple fractures by the order of only
`14%. This demonstrates that transversely fractured horizontal
`wellbores have limited capacities to resist the initiation of multi-
`ple fractures from adjacent perforations or intersecting hetero-
`geneities. Petroleum engineers can use the multiple fracture ini-
`tiation criterion when designing hydraulic fracture treatments to
`establish injection pressure limits, above which additional multi-
`ple fractures will initiate and propagate from the wellbore.
`
`Introduction
`
`A significant proportion of the worldwide recoverable hydro-
`carbon resource exists in reservoirs possessing permeabilities of
`less than one milli-Darcy (mD). At present, low production rates
`accompanying such poor permeabilities imply that, if hydrocar-
`bons are to be exploited economically, some form of permeability
`enhancement or stimulation must be carried out within these
`reservoirs. Even where initial permeabilities are relatively high,
`stimulation may still be required to overcome problems associated
`with localised permeability damage due to, for example, drilling
`mud invasion. Matrix acidisation and hydraulic fracturing remain
`the principal reservoir stimulation techniques.
`The advantages of horizontal wells in comparison with vertical
`wells have been extensively documented. Indeed, in an increasing
`number of fields throughout the world, the production of hydro-
`carbons is performed exclusively through horizontal wells. Whilst
`still a relatively rare form of completion, fractured horizontal
`wells are becoming more common in low permeability forma-
`tions. This is particularly so where surface geographies dictate
`that wells must deviate from central drill pads, such as in offshore
`
`FIGURE 1: Longitudinal fracture configuration.
`
`or arctic regions.
`Hydraulic fractures, regardless of their origin, always attempt
`to propagate in planes orthogonal to the minimum horizontal
`stress, in what is commonly referred to as the “preferred fracture
`plane.” However, while hydraulic fracture propagation planes are
`fixed, the horizontal wellbores from which they emanate may
`assume completely arbitrary orientations. Two limiting wellbore-
`fracture configurations are the focus of much attention:
`• “Longitudinal Fractures” propagate in planes parallel with
`wellbore axes, as illustrated in Figure 1. They form where
`horizontal wells are drilled parallel with the larger of the
`horizontal stresses (or parallel with the preferred fracture
`plane);
`• “Transverse Fractures” propagate in planes orthogonal to
`wellbore axes, as illustrated in Figure 2. They form where
`horizontal wells are drilled perpendicular to the larger of the
`horizontal stresses (or perpendicular to the preferred fracture
`plane).
`A number of studies have been carried out, comparing the pro-
`duction characteristics between fractured horizontal wells and
`fractured or unfractured vertical wells(1-5). In homogeneous reser-
`voirs, longitudinally fractured horizontal wells offer no apprecia-
`ble productive advantage over similarly fractured vertical wells.
`Only in thin, high permeability formations will longitudinally
`fractured horizontal wells significantly outperform fractured verti-
`cal wells(1).
`Alternatively, transversely fractured wells have the ability to
`greatly increase production rates by virtue of the fact that any
`number of fractures may be widely distributed along the length of
`horizontal wells, as illustrated in Figure 2, through multi-stage
`treatments. The reduced contact areas between horizontal well-
`
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`FIGURE 2: Transverse fracture configuration.
`
`bores and transverse fractures introduce additional “choke skin
`effects(2),” which hinders productivity and increases injection
`pressures. In general, at least three transverse hydraulic fractures
`are required to outproduce a single vertical well stimulated with
`similar dimensioned hydraulic fractures(6, 7).
`Unfortunately, transversely fractured horizontal wellbores are
`still plagued by a number of problems, most of which stem from
`the complex fracture geometries connecting the wellbore to the
`main fracture. These complex fracture geometries usually take the
`form of multiple fractures, twisted fractures, H- or S-shaped frac-
`tures(8, 9).
`The above complex fracture geometries are more commonly
`collectively known as “near wellbore tortuosity,” and result in
`narrower than anticipated fracture widths. Near-wellbore tortuosi-
`ty ultimately leads to unacceptably high fracture treatment pres-
`sures, proppant bridging and pre-mature near-wellbore screenout,
`shorter than expected final fracture lengths, and poor fracture con-
`ductivities. The origin of these fracture complexities may be
`traced back to the manner in which hydraulic fractures initiate
`from the wellbore. A considerable amount of research is currently
`devoted to understanding the dynamics of hydraulic fracture initi-
`ation. Indeed, many recently adopted field practices, such as well-
`bore break-down using highly viscous fluids(10), and decreased
`perforation densities(11), minimise fracture tortuosity by control-
`ling the fracture initiation process.
`A number of researchers(11-14), have suggested that every for-
`mation possesses an inherent “critical” or “threshold” fracture
`fluid injection pressure, above which secondary (or “auxiliary”)
`hydraulic fractures may initiate from natural fractures intersecting
`the main hydraulic fracture or wellbore. Formations with low
`threshold pressures may be susceptible to severe multiple fractur-
`ing and short overall hydraulic fracture lengths.
`The presence of such threshold pressures can be recognised as
`the flat sections on log-log plots of injection pressure vs. time.
`Nolte and Smith(12) suggested that flaws such as natural fractures
`behave as “pressure regulators,” which dilate and increase fracture
`fluid leak-off as fluid injection pressures approach threshold pres-
`sures. In addition, both Nolte & Smith(12) and Warpinski(14)
`derived criteria determining the conditions required to dilate nat-
`ural fractures intersecting main hydraulic fractures. Wells which
`have been hydraulically fractured in formations in the Wattenberg
`field of the Denver Basin in the United States display symptoms
`of natural fracture dilation with increasing fluid injection
`pressures(14).
`As a contribution to the above theories, this paper presents the
`results of analytical work carried out in order to establish the hori-
`zontal wellbore fluid pressures required to initiate additional,
`closely-spaced transverse multiple fractures from horizontal well-
`bores. In addition, the results of a series of unique laboratory mul-
`tiple fracture initiation tests are presented that provide support for
`the analytical work.
`
`Theoretical Considerations
`The stress state at the wall (in the direction of σL) of a pres-
`surised wellbore may be described in cylindrical coordinates by
`the following expressions:
`
`October 2001, Volume 40, No. 10
`
`FIGURE 3: Stresses at the wellbore wall.
`
`σ
`
`r
`
`wP=
`
`..................................................................................................(1)
`
`σ
`
`θ =
`
`σ
`3 L
`
`−
`
`σ
`
`−
`
`l
`
`wP
`
`σ
`
`zz
`
`=
`
`σ
`
`z
`
`(
`
`
`v2
`
`σ
`
`−
`
`−
`
`L
`
`σ
`
`l
`
`..............................................................................(2)
`)
`
`.......................................................................(3)
`
`where:
`σr
`= radial stress;
`σθ = tangential stress;
`σzz = wellbore axial stress;
`σL = larger in situ stress acting orthogonal to the axis of an
`arbitrarily oriented wellbore;
`σl
`= smaller in situ stress acting orthogonal to the axis of an
`arbitrarily oriented wellbore;
`σz
`= in situ stress acting along the axis of an arbitrarily orient-
`ed wellbore;
`Pw = wellbore fluid pressure;
`= Poisson’s ratio.
`v
`Compressive stresses are taken as positive. Figure 3 shows the
`orientation of the stresses described in Equations (1) to (3) on the
`wellbore wall. The classic Hubbert and Willis(15) expression,
`which makes use of Equation (2), has historically been used to
`estimate the wellbore fluid pressures required to initiate tensile
`hydraulic fractures from vertical wellbores:
`
`i
`Pwp
`
`≥
`
`3σ
`
`h
`
`−
`
`σ
`
`H
`
`+
`
`σ
`
`t
`
`...........................................................................(4)
`
`where:
`σH = maximum in situ horizontal stress;
`σh = minimum in situ horizontal stress;
`σt
`= rock tensile strength; and
`Pi
`wp = wellbore fluid pressure required to initiate a single
`(primary) fracture.
`This expression assumes that fractures form when the tangen-
`tial stress on the wellbore wall exceeds the rock tensile strength,
`and ignores the influence of pore pressure. Haimson and
`Fairhurst(16) derived a similar expression which accounted for
`poroelastic effects.
`Under the stress conditions usually prevailing at the wellbore
`wall during fracture initiation, the tangential and radial (equiva-
`lent to wellbore fluid pressure) stresses generally assume the roles
`of minor and major principal stresses respectively:
`
`σ
`
`r
`
`>
`
`σ
`
`zz
`
`>
`
`σθ
`
`........................................................................................(5)
`That is, the wellbore axial stress (σzz) is the intermediate princi-
`pal stress. The classic Hubbert and Willis expression [Equation
`
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`FIGURE 4: Stresses acting upon secondary fractures initiating in
`close proximity to a primary fracture.
`
`FIGURE 5: Distribution of stresses acting orthogonal to the plane
`of a radial, uniformly pressured fracture.
`
`As described previously by Equation (5), the radial (σr), axial
`(σzz) and tangential stresses (σθ) at wellbore walls assume the
`roles of major, intermediate and minor principal stresses, respec-
`tively, at depths typically of interest to the petroleum industry.
`Recall that, at the wellbore wall, radial stress is equivalent to well-
`bore fluid pressure. Therefore, in terms of the stresses acting on
`wellbore walls at failure, octahedral shear and normal stresses
`may be defined as follows:
`
`.........................(9)
`
`(
`
`i
`P
`wp
`
`−
`
`σ
`
`zz
`
`) +
`
`2
`
`(
`
`σ
`
`) +
`
`2
`
`(
`
`−
`
`σ
`
`θ
`
`zz
`
`σ
`
`θ
`
`−
`
`i
`P
`wp
`
`)
`
`2
`
`1 3
`
`τ
`
`oct
`
`=
`
`...................................................................(10)
`
`i
`P
`wp
`
`+
`
`σ
`
`+
`
`σθ
`
`zz
`
`)
`
`(
`
`1 3
`
`σ
`
`oct
`
`=
`
`where Pi
`wp is the wellbore fluid pressure required to initiate a sin-
`gle (primary) fracture. In addition, where the wellbore is oriented
`in a principal in situ stress direction, the tangential stress may be
`expressed in terms of the in situ stresses acting orthogonal to the
`wellbore axis, and the wellbore fluid pressure:
`
`σ
`
`θ =
`
`σ
`3 l
`
`−
`
`σ
`
`−
`
`iP
`wp
`
`L
`
`..........................................................................(11)
`
`By substituting Equations (9), (10) and (11) into the Drucker
`and Prager expression [Equation (6)], the following modified
`expression is derived:
`
`(
`
`) +
`
`2
`
`(
`
`σ
`
`−
`
`σ
`
`−
`
`3
`
`
`
`+
`
`) +
`
`2
`
`(
`
`σ
`
`3
`
`−
`
`σ
`
`−
`
`2
`
`L
`
`) =
`
`2
`
`(4)] ignores the influence of the intermediate principal stress.
`However, where secondary fractures are forced to initiate in the
`presence of a primary fracture (illustrated in Figure 4), the well-
`bore axial stress (intermediate principal stress) must play some
`role. Therefore, any criteria estimating the conditions leading to
`the initiation of closely-spaced secondary fractures must incorpo-
`rate intermediate principal stresses.
`The influence of the intermediate principal stress on rock fail-
`ure has been the subject of debate for a number of years.
`Experimental work carried out to establish the role of intermediate
`principal stresses on material failure requires relatively complex
`poly-axial test apparatus of the type used by Mogi(17). As the
`influence of the intermediate principal stress is expected to be
`subtle, highly accurate load measurement is required. This is in
`contrast with the more widely used and simpler tri-axial tests, in
`which the intermediate and minor principal stresses are assumed
`to be equal. In addition, the highly anisotropic nature of rock com-
`pounds the difficulties associated with understanding the role of
`intermediate principal stresses on rock failure. Despite the diffi-
`culties, experimental work, such as that performed by Mogi, sug-
`gests that increasing intermediate principal stresses (while main-
`taining constant minor principal stresses) increases the magni-
`tudes of major principal stresses at failure. Mogi also demonstrat-
`ed that the degree to which the intermediate principal stress influ-
`ences rock failure is closely linked to lithology.
`The Drucker and Prager(18) failure criterion (often referred to as
`the “Extended von Mises criterion”), which accommodates the
`influence of the intermediate principal stress, may be used as the
`basis of a secondary fracture initiation criterion. The Drucker and
`Prager failure criterion may be simply defined by the following
`expression:
`
`zz
`
`zz
`
`+σ σ
`l
`
`L
`
`i
`P
`wp
`
`l
`
`i
`P
`wp
`
`i
`P
`wp
`
`1 3
`
`+
`
`τ
`
`o
`
`(
`
`σ
`
`3
`
`l
`
`ψ
`3
`
`−
`
`σ
`
`L
`
`+
`
`σ
`
`ZZ
`
`)
`
`...................................................................(12)
`
`The above expression may be solved for Pi
`wp.
`The wellbore axial stress (σzz) is a function of primary fracture
`proximity (2s) and pressure (Pfp). The local stresses exerted by
`radial fractures may be described analytically, such as by solu-
`tions derived by Sneddon(21), which is illustrated graphically in
`Figure 5. This figure demonstrates that localised stress increases
`induced by hydraulic fractures diminish rapidly with increasing
`distance away from the fractures. Therefore, unless secondary
`fractures initiate within close proximity to a primary fracture, the
`wellbore pressures required to initiate secondary fractures will be
`no greater than those required to initiate single, isolated hydraulic
`fractures. However, in many cases, particularly where the pres-
`surised intervals in horizontal wells are small, or during the
`hydraulic fracturing of vertical wells, secondary hydraulic frac-
`
`τ
`
`oct
`
`=
`
`τ ψσ+
`
`
`o
`
`oct
`
`..................................................................................(6)
`
`where:
`toct = “octahedral shear stress”
`
`(
`
`σ
`
`1
`
`−
`
`σ
`
`2
`
`) +
`
`2
`
`(
`
`σ
`
`−
`
`σ
`
`3
`
`2
`
`) +
`
`2
`
`(
`
`σ
`
`−
`
`σ
`
`3
`
`)
`
`2
`
`1
`
`1 3
`
`=
`
`...........................(7)
`σoct = “octahedral normal stress” (or “mean stress term”)
`
`+
`
`σ
`
`2
`
`+
`
`σ
`
`)
`
`3
`
`(
`
`σ
`
`1
`
`1 3
`
`=
`
`......................................................................(8)
`τo and ψ are material properties which must be determined experi-
`mentally. σ1, σ2 and σ3 are the major, intermediate and minor
`principal stresses, respectively. This criterion is widely used as a
`means of assessing wellbore stability(19, 20).
`
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`TABLE 1: Summary of the laboratory-scale fracture test parameter, and comparisons with field dimensions.
`
`Parameter
`
`Wellbore Dimensions:
`Wellbore radius, rw (m)
`
`Reservoir Properties:
`Permeability, K (mD)
`
`Geomechanical Properties:
`Elastic modulus, E (MPa)
`Poisson’s ratio, v
`Fracture toughness, KIc (
`
`MPa m
`
`)
`
`Laboratory-Derived Drucker & Prager Parameters:
`τo
`ψ
`
`In situ Stresses:
`Vertical in situ stress, σv (MPa)
`Min. in situ horiz. Stress, σh (MPa)
`Max. in situ horiz. Stress, σH (MPa)
`
`Hydraulic Fracture Treatment Data:
`m/
`s
`)
`Leak-off, kl (
`Injection rate, Q (m3/s)
`Injection period, t (min)
`Fracture fluid viscosity, m (Pa s)
`
`Field-Scale Dimension
`
`Lab.-Scale Dimension
`
`0.091
`
`0.1
`
`50,000
`0.25
`3
`
`64
`47
`57
`
`4.8e-5
`0.072
`27
`0.5
`
`0.006
`
`8e-5
`
`700
`0.2
`0.27
`
`7.72
`0.73
`
`7
`5
`6
`
`3.8e-8
`3e-7 - 1e-6
`1
`30 (@ 23˚ C)
`
`Laboratory-Scale Fracture Studies
`Experimental Set-up
`A series of laboratory-scale hydraulic fracture experiments
`have been carried out in an attempt to model the initiation and
`propagation of, and interaction between, multiple transverse frac-
`tures. Only the fracture initiation aspects of the experimental work
`will be described in this paper. The fracture propagation issues
`will be discussed in future publications.
`In order to produce representative results, the laboratory tests
`adhered to the strict scaling procedures outlined by de Pater et
`al.(22) The laboratory test dimensions were scaled upon those typi-
`cally encountered during the exploitation of low permeability gas
`resources in Central Australia. Length dimensions were scaled
`according to wellbore radius (rw). Extremely low injection rates
`were employed in order to achieve stable fracture initiation and
`growth. This necessitated the use of an extremely high viscosity
`fracture fluid and a low leak-off fracture medium. Correct scaling
`also required that the fracture medium possess a low modulus (E)
`and toughness (KIC).
`A high viscosity (30 Pa•s at 23˚ C) industrial lubricant was
`employed as a fracture fluid. The fracture test material was a
`Portland cement-based material composed of the following:
`
`30%*
`Off-white Portland cement
`70%*
`Silica flour
`0.35*
`Water/cement ratio
`Acrylic emulsion/water ratio: 1:7.1*
`Water Reducing Agent:
`2,000 ml/100 kg Portland cement
`
`(* by weight of total cementicious material)
`The low cement content ensured that the fracture test material
`possessed a low elastic modulus (7,000 MPa) and low toughness
`(0.27
`). In addition, the high proportion of silica flour
`MPa m
`and inclusion of acrylic emulsion provided the test material with a
`negligible permeability (8e-5 mD). Table 1 summarises laboratory
`test material properties, and compares them with those in the field.
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`tures may indeed be forced to initiate in close proximity to prima-
`ry fractures. In addition, primary fractures initiated from wells in
`formations unbounded by more highly stressed intervals may
`grow to significant radii prior to secondary fracture initiation.
`Where secondary fractures initiate close to a primary fracture,
`the wellbore axial stress (σzz), against which the secondary frac-
`ture must form, approaches that of the primary fracture pressure.
`Under such ‘zero-spaced’ conditions, the single fracture Drucker
`and Prager criterion described by Equation (12) can be modified
`such that it assumes the following form:
`
`P
`
`fp
`
`−
`
`
`
`+σ σ
`l
`
`3
`
`L
`
`+
`
`i
`P
`ws
`
`) +
`
`2
`
`(
`
`σ
`
`3
`
`l
`
`−
`
`σ
`
`L
`
`−
`
`2
`
`i
`P
`ws
`
`) =
`
`2
`
`(
`
`−
`
`i
`P
`ws
`
`P
`
`fp
`
`) +
`
`2
`
`(
`
`1 3
`
`+
`
`τ
`
`o
`
`(
`
`ψ
`3
`
`σ
`
`3
`
`l
`
`−
`
`σ
`
`L
`
`+
`
`fpP
`
`)
`
`....................................................................(13)
`
`where:
`Pfp = uniform primary fracture pressure;
`Pi
`ws = wellbore pressure required to initiate secondary hydraulic
`fracture.
`Equation (13) can then be solved for Pi
`ws. In the field, however,
`individual hydraulic multiple fractures are not hydraulically iso-
`lated. This is in contrast with the ‘static’ multiple fracture initia-
`tion described by Equation (13). Indeed, the fluid pressures within
`the primary and secondary fractures are coupled. Thus the modi-
`fied Drucker and Prager multiple fracture initiation criterion
`described by Equation (13) must be solved iteratively. The
`dynamic solution process simply involves substituting, at each
`iteration, the wellbore pressure required to initiate a secondary
`fracture (Pi
`ws), into the uniform pressure within the primary frac-
`ture (Pfp). This process is repeated until convergence.
`
`October 2001, Volume 40, No. 10
`
`

`

`pressure record for multiple fracture Test #3 is illustrated in
`Figure 9. The fracture pressures displayed in Figure 9 have been
`corrected for compressibility of the injection system and fracture
`fluid. During injection testing, both wellbores were pressurised at
`similar rates. A primary fracture eventually initiated from one of
`the two wellbores. Immediately after the primary fracture initiat-
`ed, the wellbore from which it emanated was shut-in. Injection
`into the primary fracture recommenced only after the secondary
`fracture (from the opposing wellbore) was initiated. Injection into
`both fractures was allowed to proceed at a constant rate for a peri-
`od of approximately two minutes, whereupon they were both
`shut-in.
`
`Results
`The Drucker and Prager material constants (τo and ψ) were
`derived through tri-axial testing of the fracture test material, and
`are listed in Table 1. By substituting these material constants and
`the applied in situ stresses (σl, σL and σz) into Equation (13), the
`following criterion is derived:
`(
`) +
`(
`) +
`
`−
`
`i
`P
`ws
`
`P
`
`fp
`
`2
`
`P
`
`fp
`
`−
`
`+
`
`11
`
`i
`P
`ws
`
`2
`
`−(
`
`11 2
`
`) =
`
`2
`
`i
`P
`ws
`
`1 3
`
`.+
`.
`7 72 0 245
`
`(
`
`)
`
`11
`
`+
`
`Pfp
`
`............................................................................(14)
`
`This criterion can be used to estimate the wellbore fluid pres-
`sure (Pi
`ws) required to initiate secondary hydraulic fractures in the
`presence of a nearby inflated primary fracture. The laboratory
`fracture test provided a unique opportunity to establish the validi-
`ty of this modified criterion.
`As described previously, field-scale primary and secondary
`fracture pressures are coupled. This contrasts with the experimen-
`tal configuration, in which the primary and secondary multiple
`fractures initiated and propagated in hydraulic isolation. However,
`
`FIGURE 6: Laboratory block configuration.
`
`The synthetic fracture test material was cast into blocks mea-
`suring 400 × 400 × 400 mm. Thin circular plastic disks were posi-
`tioned inside the blocks during casting (Figure 6). When intersect-
`ed by a wellbore, these disks constrained the location at which
`hydraulic fractures initiated. The disks were separated by a dis-
`tance 30 mm, and were intersected by two, hydraulically isolated
`wellbores, each possessing a radius of 6 mm. Stainless steel injec-
`tion tubes, of 3 mm internal radius, were grouted into the well-
`bores, leaving a small “open hole” section immediately adjacent
`to the plastic disks. The absence of a sand fraction left the synthet-
`ic fracture medium susceptible to shrinkage cracking. However,
`this was minimised by storing the blocks under conditions of
`100% humidity during curing, and until immediately prior to
`testing.
`
`The blocks were placed in a poly-axial cell, as illustrated in
`Figure 7. Through the use of water-filled flat-jacks, the poly-axial
`cell exerted stresses on all faces of each block. The magnitudes of
`the applied stresses (Table 1) were such that the wellbores were
`oriented in the direction of the minor principal stress. This orien-
`tation between wellbore and stresses promoted the formation of
`transverse hydraulic fractures. Two computer-controlled linear
`displacement pumps, shown in schematic form in Figure 8, were
`used to inject fracture fluid independently into each wellbore. In
`addition, transducers independently measured the initiation and
`propagation pressures of each multiple fracture. The injection
`
`FIGURE 7: Poly-axial cell configuration.
`
`FIGURE 8: Schematic of the laboratory hydraulic fracture
`injection and data recording systems.
`
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`FIGURE 9: Injection pressure record for the laboratory multiple fracture initiation and propagation test #3.
`
`ple fractures from adjacent perforations or intersecting hetero-
`geneities. That is, second, third, and fourth, etc., generation
`hydraulic transverse fractures will be generated, in turn, as the
`wellbore pressure reaches the required threshold pressure (Pi
`ws).
`This study contributes to previous works by establishing the
`wellbore pressures at which additional multiple fractures will ini-
`tiate from an initially intact wellbore. Such information may be
`invaluable where transversely fractured horizontal wells are to be
`completed in naturally fractured formations. It is emphasized,
`however, that this technique is yet to be trialled in the field. Such
`a trial may be performed on a single horizontal wellbore, and will
`require measurement of Drucker and Prager material constants of
`the formation and a means of detecting or inferring the presence
`of multiple hydraulic fractures, through net treating pressure
`analysis.
`A hypothetical fracture injection pressure profile is shown in
`Figure 10, based on the average initiation and propagation pres-
`sures of transversely fractured horizontal wells in the North Sea(9).
`The measured average fracture initiation pressure was of the order
`of 46.54 mPa (6,750 psi). Therefore, according to the modified
`Drucker and Prager criterion [Equation (13)], it is estimated that
`secondary multiple fractures will initiate if the bottom hole treat-
`ing pressure is allowed to exceed 53.06 mPa (7,695 psi). Such
`
`due to the modest impact of the intermediate principal stress on
`fracture initiation pressures, the difference between the iterative
`and static solutions of Equation (14) should not be unduly large.
`Thus Equation (14) was solved in a static fashion to arrive at a
`secondary fracture initiation pressure (Pi
`ws) of 22.4 MPa. The theo-
`retical Drucker and Prager primary (or single) fracture initiation
`pressure (Pi
`wp) for the laboratory test may be easily derived
`through use of Equation (12), though with the wellbore axial
`stress (σzz) estimated through use of Equation (3). Accordingly,
`the analytically derived ratio of secondary to primary fracture
`
`for the DC-3 laboratory configuration
`
` 
`
`i w
`P P
` 
`
`ws
`i
`
`p
`
`initiation pressure,
`was 1.14.
`
`The experimentally-derived ratio of secondary to primary frac-
`ture initiation pressure for Test DC-3 was approximately 1.08.
`The reason for the slight disparity between the analytically deter-
`mined (1.14) and experimentally measured (1.08) secondary to
`primary fracture initiation pressure ratios is most likely due to
`some incorrect assumptions regarding the experimental work. The
`analytical Drucker and Prager solution [Equation (14)] assumes
`that the primary fracture is uniformly pressurised to a degree
`equal to its break-down pressure (20.45 MPa). However, perusal
`of the experimental pressure plot (Figure 13) indicates that upon
`shut-in, the primary fracture pressure decreased significantly. By
`the time the secondary fracture initiated, the primary fracture pres-
`sure had decreased from 20.45 MPa to 14.9 MPa. Therefore, if Pfp
`= 14.9 MPa is substituted into Equation (14), the analytically
`
`i w
`P P
`
`ws
`i
`
`derived ratio of
`
`equals 1.11, which compares more closely
`
`p
`with the experimentally determined ratio of 1.08.
`It is important to note that this criterion deals with fracture ini-
`tiation, and as such makes no comment regarding the eventual
`size of secondary hydraulic fractures in comparison with the pri-
`mary fracture. The exact size and distribution of multiple
`hydraulic fractures is still the source of constant debate, and was
`beyond the scope of this study.
`
`Discussion
`The reasonable agreement between the analytical estimates and
`experimental measurements of secondary fracture initiation pres-
`sure provides confidence in the validity of the modified Drucker
`and Prager criterion [Equation (14)]. Both the multiple fracture
`initiation criterion and the laboratory results suggest that close
`proximity of primary hydraulic fractures increases the initiation
`pressures of secondary multiple fractures by the order of only
`14%. This demonstrates that transversely fractured horizontal
`wellbores have limited capacities to resist the initiation of multi-
`
`October 2001, Volume 40, No. 10
`
`FIGURE 10: Hypothetical injection pressure record, illustrating of
`the onset of secondary fracture initiation with increasing wellbore
`pressure. Primary fracture initiation and propagation magnitudes
`are based on field data obtained during the treatment of
`transversely fractured horizontal wells in the North Sea(9).
`Secondary fracture initiation pressures were estimated through
`use of the modified Drucker and Prager criterion [Equation (13)].
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`high fracture propagation pressures will occur if fractures are
`propagated through highly confined formations or in the presence
`of perforation or fracture tortuosity flow restrictions. Field evi-
`dence(8) suggests that the formation of multiple hydraulic fractures
`from such completions is particularly detrimental to successful
`fracture treatments and post-fracture productions. Fracture design
`engineers can use secondary fracture initiation pressures furnished
`by the modified Drucker and Prager criterion to design fracture
`treatments that maintain fracture and wellbore pressures below
`that required to initiate additional multiple hydraulic fractures.
`Such limiting injection pressures will be a complex function of in
`situ stress distribution, reservoir thickness and rock properties.
`Modified fracture designs may incorporate reduced fluid injection
`rates or fracture fluid viscosities, which can result in final
`hydraulic fracture lengths which are significantly smaller than
`those originally desired. The alternative to limiting the generation
`of mulitple secondary fractures is the increased risk of premature
`screen-out, or time-consuming and costly proppant slug exercises.
`
`Conclusions
`1. A criterion, based on that by Drucker and Prager, has been
`derived, which predicts the wellbore pressures required to
`initiate secondary multiple transverse hydraulic fractures in
`close proximity to primary fractures.
`2. Secondary fracture initiation pressures predicted by this new
`criterion compares reasonably well with those measured dur-
`ing laboratory-scale multiple hydraulic fracture interaction
`tests.
`3. Both the multiple fracture initiation criterion and the labora-
`tory results suggest that close proximity of primary
`hydraulic fractures increases the initiation pressures of sec-
`ondary multiple fractures by the order of only 14%. This
`demonstrates that transversely fractured horizontal wellbores
`have limited capacities to resist the initiation of multiple
`fractures from adjacent perforations or intersecting
`heterogeneities.
`4. Designers of hydraulic fracture treatments can use the multi-
`ple fracture initiation criterion to establish injection pressure
`limits (or “threshold pressures”), above which additional
`multiple fractures will initiate and propagate from the well-
`bore. Such a tool may be particularly useful in the design
`and treatment of transverse fractures from horizontal well-
`bores, which are particularly prone to complications associ-
`ated with multiple fracturing.
`
`Acknowledgements
`The authors wish to acknowledge the Australian Petroleum
`Cooperative Research Centre (APCRC) for supporting this work
`and CSIRO Petroleum for use of their laboratory facilities in
`Melbourne.
`
`NOMENCLATURE
`= wellbore radius;
`rw
`s
`= half-distance between primary fracture and site of
`secondary fracture initiation;
`υ
`= Poisson’s ratio;
`Pfp = primary fracture pressure;
`Pw = wellbore fluid pressure;
`Pi
`wp = wellbore pressure required to initiate a single (primary)
`hydraulic fracture;
`Pi
`ws = wellbore pressure required to initiate secondary hydraulic
`fracture;
`= hydraulic fracture radius;
`Rf
`σ1 = major principal stress;σ
`σ2 = intermediate principal stress;
`σ3 = minor principal stress;
`σv = vertical in situ stress;
`
`σH = maximum horizontal in situ stress;
`σh = minimum horizontal in situ stress;
`σz
`= in situ stress acting along the axis of an arbitrarily
`oriented wellbore;
`σzz = axial wellbore stress;
`σl
`= smaller in situ stress acting orthogonal to the axis of an
`arbitrarily oriented wellbore;
`σL = larger in situ stress acting orthogonal to the axis of an
`arbitrarily oriented wellbore;
`σr
`= radial stress;
`σt
`= rock tensile strength;
`σθ = tangential stress;
`τoct = octahedral shear stress;
`σoct = octahedral normal stress;
`τo
`= Drucker and Prager material constant;
`ψ = Drucker and Prager material constant;
`
`SI Metric Conversion Factors
`ft × 3.048*
`E + 00 = m
`in × 2.54*
`E + 00