SPE 29443
`
`A Case History of Completing and Fracture Stimulating a Horizontal Well
`
`Hazim H. Abass,** Peter Hagist,* James Harry,t James L. Hunt,** Mark Shumway,t Naz Gazi**
`*Pennzoil, **Halliburton Energy Services, tChoctaw II Oil and Gas, Ltd
`
`SPE Members
`
`Copyright 1995, Society of Petroleum Engineers Inc.
`
`This paper was prepared for presentation at the 1995 SPE Production Operations Symposium, Oklahoma City, April 2-4.
`
`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 of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject
`to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its
`officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petro-
`leum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract
`should contain conspicuous acknowledgment of where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box
`833836, Richardson, TX 75083-3836, U.S.A. Telex, 730989 SPEDAL
`
`Abstract
`
`Introduction
`
`This paper presents a detailed description of the
`completion and fracture stimulation of a high-angle
`well in the Madison formation of the Williston Basin in
`North Dakota. The case history of the Candee 26-13
`HA well is used. The completion and fracture stimula-
`tion techniques used on this well resulted in a three and
`a half-fold increase in the ultimate recovery of the well,
`in comparison to a vertical well in the same field.
`
`The well was directionally drilled to intersect natural
`fractures and provide optimal conditions for hydraulic
`fracture stimulation. To ensure zone selectivity and
`isolation, the well was cased and cemented. Notching
`techniques were used to allow hydraulic fracture
`treatments to be selectively initiated along the wellbore.
`Matrix acidizing was an essential phase to achieve this
`goal.
`
`This paper also presents a discussion of how reservoir
`simulators can be used to optimize the number of
`fractures needed to cover a given drainage area. In
`addition, prefracture and postfracture evaluations are
`discussed.
`
`The primary benefit of drilling a horizontal well is to
`take advantage of a greater effective drainage area than
`that available from a vertical well drilled in the same
`area. Fracturing a horizontal well has presented prob-
`lems because of premature screenouts and high treat-
`ment pressures. In most geological formations, the
`orientation angle of a horizontal well from the maxi-
`mum horizontal stress plays a crucial role in achieving
`a successful stimulation treatment. The following three
`mechanisms related to wellbore orientation relative to
`the maximum horizontal stress (orientation angle) need
`to be addressed.'
`
`• Fracture-wellbore communication area. Two
`extreme cases, longitudinal and orthogonal frac-
`tures, provide maximum (longitudinal) and mini-
`mum (orthogonal) communication area between the
`wellbore and propagating fractures.
`• Fracture geometry near the wellbore. Fracture
`geometry is an important factor that may cause
`early screenouts. Several different fracture geom-
`etries can result when a horizontal well is fractured,
`including multiple fractures, T-shaped fractures,
`and complex fractures.
`
`References at the end of the paper.
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`2
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`A Case History of Completing and Fracture Stimulating a Horizontal Well
`
`SPE 29443
`
`northwest-southeast trending anticlinal feature in a
`position where significant fracture enhancement occurs
`because of structural flexure. The wellbore was drilled
`parallel to the least principal stresses in an east-west
`direction across the northern nose of the structure. The
`principal stress directions were determined from
`structural analysis and regional fracture directions
`(Fig. 1). The pay zone consisted of approximately 125
`ft of primarily fractured carbonate with 4 to 6 ft of 10%
`porous limestone in the Ratcliffe formation. Fig. 2
`shows a schematic of the wellbore.
`
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`as at 691
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`• Stimulation zone
`
`• Fracture tortuosity near the wellbore. This phe-
`nomenon occurs when the wellbore is oriented in
`such a way that the fracture must go through a
`reorientation process. This process results in
`fracture surface roughness, which restricts flow and
`can cause premature screenout.
`
`Soliman et al.2 discussed the situation in which multiple
`fractures are created from a horizontal wellbore. They
`used an analytical model to show the effect of fracture
`conductivity near the wellbore on production perfor-
`mance. The optimum number of fractures along the
`horizontal wellbore for a given drainage area was also
`discussed.
`
`Austin et al.3 emphasized the importance of casing and
`cementing the horizontal section to allow for fracture-
`initiation points to place multiple fractures along the
`horizontal well. Overbey et al.', presented a case
`history on using external casing packers to divide the
`horizontal section into several zones for fracture
`stimulation. The objective of their work was to propa-
`gate natural fractures and induce additional fractures at
`each interval.
`
`Owens et al.s presented an application of the tip
`screenout technique in fracturing horizontal wells. The
`information presented in this paper is based on more
`than 100 propped fracture treatments placed from
`horizontal wells.
`
`The main issues discussed in Reference 5 are (1) the
`importance of casing and cementing for isolation and
`(2) performing a good cement job at the interval of
`fracture initiation to help prevent multiple fractures.
`Stoltz' presented case studies of two horizontal wells
`used for enhanced oil-recovery purposes.
`
`Background
`
`The objective of the Candee 26-34HA project was to
`determine if a single, high-angle well drilled through
`the Ratcliffe and Mission Canyon formations of the
`Williston Basin could recover reserves equal to the
`reserves recovered from two to three vertical wells
`completed through the same interval. The test well was
`spudded on Dec. 27, 1990, and drilled to a total depth
`of 9,330 ft on Feb. 6, 1991. Total measured depth was
`12,115 ft with a lateral offset of 3,300 ft. A 5 1/2-in.
`casing was cemented to TD. The well is located on a
`
`Fig. 1—The principal stress directions determined from
`structural analysis and regional fracture directions.
`
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`H.H. Abass, P. Hagist, J. Harry, J.L. Hunt, M. Shumway, N. Gazi
`
`9,400
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`Total Departure (ft)
`---- Measured Depth
`— True Vertical Depth
`
`3,000
`
`4.000
`
`Fig. 2—Wellbore schematic.
`
`Reservoir Considerations
`
`Generally, hydraulic fracturing of a horizontal well is
`indicated under certain conditions. These conditions
`include restricted vertical flow, such as those caused by
`low vertical permeability or impenetrable shale streaks
`within the productive interval, attempting to intercept
`swarms of natural fractures with random orientation,
`and zones with low productivity and/or low permeabil-
`ity.
`
`Once the need for fracturing is established, the orienta-
`tion of the fractures with respect to the horizontal
`wellbore must be addressed. Ideally, this decision
`should be made before the horizontal section is drilled,
`since the induced fracture direction depends on the
`orientation of the principal stresses. Fracture orienta-
`tion can be classified as either longitudinal (where the
`fracture axis coincides with the wellbore axis) or
`transverse (where the fracture axis is perpendicular or
`generally at some angle to the wellbore). Fracture
`orientation is usually based on reservoir and fracture
`performance considerations.
`
`The main criterion for transverse vs. longitudinal
`fractures is the dimensionless fracture conductivity,
`CFd, as defined by the following equation:
`
`CFd
`
`
`
`k fb
`kL
`
`(1)
`
`Physically, the CFd compares the flow capacity within
`the fracture to the flow capacity of the formation along
`the fracture length. High CFds indicate excess flow
`capacity within the fracture, meaning that the fracture's
`
`capability to deliver reservoir fluid to the wellbore is
`high relative to the formation's capability to deliver
`reservoir fluid to the fracture. This behavior suggests
`little flow restriction within the fracture. Low Cads
`indicate the opposite: the formation's capability to
`deliver reservoir fluid to the fracture is high relative to
`the fracture's ability to deliver that fluid to the well-
`bore. This behavior implies flow restriction within the
`fracture. When transverse vs. longitudinal fractures are
`considered, it has been reported that longitudinal
`fractures are advantageous when the C. is less than 5
`to 10. Transverse fractures are advantageous when the
`CFd is greater than 5 to 10.2.8
`
`An additional reason for selecting transverse fractures
`is that a horizontal well containing multiple transverse
`fractures has the potential of contacting more reservoir
`area than a horizontal well containing longitudinal
`fractures. The additional "reach" associated with
`transverse fractures allows accelerated recovery of the
`reservoir, especially in the area between the fractures at
`early times. Low-permeability reservoirs will benefit
`from this completion option.
`
`Certain characteristics of transverse fractures should be
`carefully considered to help ensure effective fracture
`completion of a horizontal wel1.48 Because of the
`geometry of a transverse fracture's relationship with a
`horizontal wellbore, the fracture's contact with the
`wellbore is limited as shown in Fig. 3, Page 4. Soliman
`et al.2 presented an early-time-transient analytical
`model for a finite conductivity transverse fracture that
`describes a linear-radial flow regime. Fluid flows from
`the reservoir linearly into the fracture. Once the fluid is
`inside the fracture, it flows radially toward the well-
`bore. The radial flow causes an additional pressure
`drop within the fracture at the wellbore called conver-
`gence skin. Economides et al .s presented the following
`equation for convergence skin factor:
`
`(S h ) =—ich rin—h
`k b L
`2r., 2j
`f
`
`(2)
`
`To overcome the convergence skin effect, high CFd is
`necessary. Soliman et al.2 showed that a high CFd tail-in
`significantly reduces the radial convergence skin effect.
`In gas wells, non-Darcy flow contributes to the conver-
`gence skin. After a fracturing treatment, high CFd is
`necessary for effective cleanup. The presence of high
`
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`4
`
`A Case History of Completing and Fracture Stimulating a Horizontal Well
`
`SPE 29443
`
`water saturation in the fracture reduces the fracture
`conductivity near the wellbore, resulting in an effect
`similar to convergence skin. Generally, transverse
`fractures need to be designed for higher CH values than
`their vertical well counterparts to overcome the limited
`contact with the horizontal wellbore.
`
`For the subject well, anticipated ;Is were well above
`the 5 to 10 range; therefore, transverse fracture geom-
`etry was selected. Evaluation of the convergence skin
`based on Eq. 2 resulted in a skin factor of 0.013,
`indicating effectively no radial convergence skin effect
`within the fracture. This result is not surprising because
`of the high anticipated CH value resulting mainly from
`the low formation permeability. Preliminary design
`indicated a fracture half-length of approximately 400 ft
`and fracture conductivity of about 1,500 md-ft, result-
`ing in a CH of more than 100. Even though the CFd is
`very favorable, it was decided to tail-in with high-
`conductivity, high-strength proppant to maintain high
`CFd in the near-wellbore region over time.
`
`Rock Mechanics Considerations
`
`When the horizontal section of a wellbore is drilled
`through the formation parallel to the direction of
`minimum horizontal stress, a
`, a transverse fracture
`should be expected during hydraulic fracturing (Fig. 4).
`Transverse fractures initiate and extend at approxi-
`mately right angles to the wellbore axis. Several
`different intervals along the horizontal wellbore can be
`stimulated for optimum reservoir depletion.
`
`A multiple fracture system might be created that could
`present complex fluid flow problems that hinder a
`successful stimulation treatment. Fig. 5 shows the
`effect of perforated interval length on the number of
`multiple fractures created. These multiple fractures can
`
`Fig. 3—Fluids radially converge in a transverse fracture
`approaching a horizontal borehole. This phenomenon
`causes an unusually high pressure drop in the fluid flow
`of horizontal wells with transverse fractures.
`
`Fig. 4—A horizontal section of a wellbore drilled through
`the formation parallel to the direction of minimum hori-
`zontal stress, alma..
`
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`H.H. Abass, P. Hagist, J. Harry, J.L. Hunt, M. Shumway, N. Gazi
`
`(a
`
`= 3a v a
`
`(4)
`
`It is obvious that (9, is less than (st)m, which suggests
`that a tensile failure at the high and low sides of the
`wellbore will initiate during hydraulic fracturing,
`creating a longitudinal fracture along the treated
`interval. This fracture will propagate in the direction
`perpendicular to the maximum horizontal stress and
`must go through a reorientation process to become
`perpendicular to the minimum horizontal stress. Frac-
`ture reorientation can result in a rough fracture surface
`that a proppant may bridge, possibly causing a
`screenout.
`
`To avoid these problems, an acid job was used to
`connect all the slots created around the wellbore and
`form a cavity. Use of this job design achieved two
`objectives:
`
`•
`
`•
`
`It encouraged the creation of a single fracture from
`the cavity surface that was oriented perpendicular
`to the minimum horizontal stress.
`It created a nonrestricted zone between the fracture
`and the wellbore.
`
`Perforation Design
`
`Perforations play a crucial role in achieving a success-
`ful fracturing treatment in horizontal wellbores. The
`design of the perforating program (phasing, number,
`size, and perforated interval length) may depend on
`fracture initiation geometry. Fracture initiation deter-
`mines the communication path between the wellbore
`and fracture plane at the wellbore. Nonplanar fracture
`geometries, such as multiple, reoriented, T-shaped, and
`other complex fractures (Fig. 6, Page 6), are not
`advantageous; they adversely affect the potential to
`achieve the required stimulation treatment. The serious
`problems that can result because of these nonplanar
`fracture geometries are listed below.
`
`• When two fractures propagate from the same
`interval, they share the same rock material as they
`are developing width. Therefore, instead of having
`a wide fracture, two narrow fractures result.
`Adequate fracture width is needed to place
`proppant slurry inside the fracture. If it is too
`narrow, proppant may bridge near the wellbore
`
`Fig. 5—Length of the perforation interval affects
`whether or not multiple fractures are created
`
`result in reduced fracture width near the wellbore,
`leading to high treating pressures and/or screenouts.
`
`In practice, it is important to have a clear communica-
`tion channel between the wellbore and the major
`fracture propagating under the effect of the unaltered
`state of stress. Therefore, fracture strands must not be
`created. To achieve this objective, the following
`arguments were considered:
`
`• Since the fracture is anticipated to initiate perpen-
`dicular to the wellbore (transverse fracture), it is
`necessary to perforate only a short interval, such as
`1 ft.
`• To avoid creating T-shaped and/or multiple frac-
`tures, it is crucial to ease the near-wellbore stress
`concentration by creating a large cavity around the
`wellbore.
`
`The cavity is assumed to dictate the fracture direction
`and communicate the small fracture width to the
`wellbore. Creation of the cavity eases the stress concen-
`tration around the wellbore, which eliminates the
`creation of a longitudinal fracture along the wellbore.
`For example, a wellbore is drilled in the direction of
`minimum horizontal stress as shown in Fig. 4. The
`tangential stress at the wellbore and at two locations, in
`the direction of vertical stress, v, and in the direction of
`maximum horizontal stress, M, are given as
`
`(a I = 3a Hmax a v
`
`(3)
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`6
`
`A Case History of Completing and Fracture Stimulating a Horizontal Well
`
`SPE 29443
`
`area, causing pressure increases that result from
`flow restriction.' Eventually, screenout occurs
`when proppant concentration and/or size is in-
`creased.
`• Fluid leakoff increases with the number of fracture
`strands, which results in reduced fluid efficiency
`and premature screenout.
`• Wall waviness of a reoriented fracture causes
`increased friction pressure, which leads to high
`treatment pressure and operational problems.
`
`Therefore, for a successful hydraulic fracturing treat-
`ment, a perforation design should be in phase with the
`anticipated fracture direction to ensure (1) a fracture
`that propagates perpendicular to the minimum horizon-
`tal stress, which gives an optimum width, (2) a single
`fracture to propagate, which creates a longer fracture,
`and (3) reduction of breakdown and extension pres-
`sures, which is preferred in any fracturing treatment.
`
`In this case, the fracture is anticipated to initiate
`perpendicular to the wellbore (transverse fracture). To
`avoid initiating multiple fractures, it is recommended to
`extensively perforate (360° phasing) a short interval (a
`few feet) of the wellbore. If the formation is a carbon-
`ate, it is recommended to start with a stage of HCI at
`the matrix flow injection rate to create a better commu-
`nication channel between the wellbore and the main
`fracture.
`
`cr,
`
`Single
`Fracture
`
`Single
`Fracture
`
`aHmax
`
`• Single
`• T-shaped
`• Multiple
`
`allmin
`• Multiple (at weUbore)
`• Reorientation
`
`• Reorientation
`• Multiple Fracture (away from weUbore)
`
`Fig. 6—Nonplanar fracture geometries.
`
`Optimizing the Number of Fractures
`
`When transverse fractures exist, a major design crite-
`rion is the optimum number of fractures to create. A
`very good indication of the most effective number of
`fractures can be determined by simulating production
`for various numbers of fractures. Economics can then
`be applied to these few cases and the most effective
`fracture number can be determined. An analytical
`model has recently been presented in the literature,9 but
`it does not consider reservoir boundaries. This model
`may be useful for investigating early-time production,
`but long-term production, including the effect of
`boundaries, must be considered before the most effec-
`tive number of fractures can be determined. Until an
`analytical model is developed that considers multiple
`fractures in a horizontal wellbore in a closed reservoir,
`numerical simulation must be used to determine the
`optimum number of fractures necessary to effectively
`produce a horizontal wellbore. A technique to deter-
`mine the optimum number of fractures with a fractured
`well numerical simulator is described in Reference 2.
`
`Optimizing the number of fractures for the subject well
`was accomplished using the technique presented in
`Reference 2. The total drainage area for the well/
`fracture system was 459 acres (4,000 ft x 5,000 ft).
`Horizontal well length was 3,000 ft, and the fractures
`considered had 400 ft half-length and were identical.
`Results of the simulation runs are presented in Fig. 7 as
`a plot of cumulative liquid production vs. the number of
`fractures for various times after fracturing. Initially, the
`relationship between cumulative production and
`number of fractures is linear because the formation has
`low permeability and each fracture is producing from
`its own drainage area with no interference from adja-
`cent areas. After a few months of production, the
`fractures establish their own drainage area and interfer-
`ence between adjacent fractures begins. After a very
`long time (much longer than shown on Fig. 7), the
`reservoir between the outermost fractures has effec-
`tively been drained, and the behavior of the system
`approaches that of a horizontal well containing a single
`fracture. Based on this behavior, the optimurn number
`of fractures is time-dependent. A time horizon needs to
`be chosen to arrive at a realistic value for the number of
`fractures that balances recovery with cost. For the
`subject well, a time of about 24 months was chosen as
`the time horizon. At 24 months (Fig. 7), the slope of the
`curve is constant up to three fractures, then it decreases
`
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`H.H. Abass, P. Hagist, I. Harry, J.L. Hunt, M. Shumway, N. Gazi
`
`and rapidly flattens after four to five fractures. Based
`on the diminishing slope of the cumulative production
`vs. time curve at 24 months, four or five fractures
`would be the most effective number of fractures for the
`subject well. However, after considering the behavior
`of the well/fracture system, designers considered
`economics and selected three fractures for the subject
`well.
`
`al MOO
`
`▪ 1,600
`
`e • 1,400
`
`1,200
`cp. 1.000
`000
`
`600
`
`400
`•
`3 200
`e°
`0
`
`0
`
`1
`
`2
`
`3
`
`7
`6
`5
`4
`Number of Fractunts
`
`it
`
`9
`
`10
`
`11 12
`
`Fig. 7—Cumulative liquid production vs. the number of
`fractures for various times after fracturing.
`
`Stimulation Treatment
`
`The stimulation treatment was designed to achieve the
`following objectives:
`
`• To create a cavity near the wellbore. To ease the
`near-wellbore restriction, an acid stage was used to
`communicate all the hydrojetted notches. Fig. 8
`presents a schematic of the longitudinal slots
`created via hydrojetting. Fig. 9 shows a conceptual
`representation of what might have happened after
`an acid treatment. Fig. 10 shows the creation of the
`main fracture as it initiates from the cavity.
`• To prevent the natural fractures intersecting the
`wellbore from initiating and propagating multiple
`fractures. For fluid-loss contol, 100-mesh sand was
`pumped after the pad.
`• To help withstand the high compressive stress near
`the wellbore and reduce the pressure drop resulting
`from the radial flow convergence. High-strength,
`coarse proppant was used as a tail-in stage.
`
`Fig. 8—Longitudinal slots created by hydrojetting.
`
`Fig. 9—Conceptual representation of what might have
`happened after an acid treatment.
`
`ON MAX
`
`Fig. 10—Creation of the main fracture as it initiates from
`the cavity.
`
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`8
`
`A Case History of Completing and Fracture Stimulating a Horizontal Well
`
`SPE 29443
`
`Based on the above guidelines, the following treatment
`design was implemented:
`
`Production Increase
`
`Treatment Materials
`
`a. 2,500 gal of 15% HCI
`b. 15,000 lb of 100-mesh sand at 1 lb/gal
`for 20,000 gal
`c. 73,700 lb of 20/40 mesh sand
`d. 27,500 lb of 16/20 mesh synthetic proppant
`
`Job Procedure
`
`a. 2,500 gal of 15% HCI
`b. 12,000 gal of prepad
`c. 25,000 gal high-temperature fracturing gel
`20,000 gal high-temperature fracturing gel with 1
`lb/gal 100-mesh sand
`400 gal spacer
`d. 12,000 gal high-temperature fracturing gel 0.25 lb/
`gal 20/40 mesh sand
`5,000 gal high-temperature fracturing gel 0.50 lb/
`gal 20/40 mesh sand
`5,000 gal high-temperature fracturing gel 0.75 lb/
`gal 20/40 mesh sand
`5000 gal high-temperature fracturing gel 1.00 lb/gal
`20/40
`e. 25,000 gal high-temperature fracturing gel ramped
`from 1 to 5 lb/gal 20/40 mesh sand
`f. 7,000 gal high-temperature fracturing gel ramped
`from 5 to 6 lb/gal 16/20 synthetic proppant
`g. 11,000 gal saltwater flush
`The injection rate was 50 bbl/min. Initial surface
`pressure was 3,050 psi during pad. At the 0.5 lb/gal
`stage, surface pressure was 2,940 psi. For job comple-
`tion and before shutdown, surface pressure was 3,580
`psi. The total volume of fluid injected was 136,162 gal.
`
`The well was completed in four intervals spaced evenly
`along the wellbore. Each interval was notched along an
`interval of no more than 2 1/2 ft, with hydrojets. The
`slots were then acidized with approximately 1,000 gal
`of 15% HCI to help ensure connectivity with the
`formation and then fracture-treated with 50,000 to
`160,000 lb of 20/40 synthetic proppant. Each interval
`was isolated and treated separately.
`
`Initial production began in July 1991 at an average
`daily rate of 290 BOPD and 300 BWPD. As of June
`1994, average daily production has declined to 80
`BOPD and 147 BWPD, and total cumulative recovery
`is now 137,000 bbl of oil. Ultimate recovery is esti-
`mated at 450,000 bbl of oil.
`
`Fig. 11 shows the projected performance of the Candee
`and the normalized production curve for the average 11
`vertical offsetting wells. A typical vertical well has an
`initial production rate of 95 BOPD and will recover
`approximately 120,000 bbl of oil over a 10- or 12-year
`economic life. The Candee, in contrast, is expected to
`recover over 450,000 bbl of oil during its economic
`life—approximately 3.5 times a typical vertical well.
`
`10,000
`
`1 MOO
`
`100
`
`_ .......
`"'"--
`..,......
`...
`
`--------
`-----------
`
`
`
`--------S Cumutetive 01 Candle Projection —
`
`,
`
`Cu
`
`alive OD—Average WWI
`
`0
`
`0
`
`10
`
`, v8y is u8 es rem ------
`Months
`— Nommated Production Curve—Avg. 11 Wells
`--- Centime 25-1311 Production
`
`Fig. 11—Projected performance of the Candee and the
`normalized production curve for the average 11
`vertical offsetting wells.
`
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`

`H.H. Abass, P. Hagist, J. Harry, J.L. Hunt, M. Shumway, N. Gazi
`
`Conclusions
`
`References
`
`• A horizontal wellbore was successfully drilled,
`completed, and fracture-stimulated in the Williston
`Basin, North Dakota.
`
`Casing and cementing a horizontal well is essential
`to provide zone selectivity and isolation during
`fracture stimulation.
`
`• Single-point initiation was necessary to success-
`fully propagate transverse fractures. A successful
`technique to hydrojet slots along the casing to
`initiate a single transverse hydraulic fracture was
`presented.
`
`• The number of transverse fractures along the
`horizontal well was optimized based on production
`increase and economics.
`• The stimulation treatment was designed to prevent
`multiple fractures, withstand the high near-wellbore
`compressive stress, and overcome the near-well-
`bore convergence skin.
`• A 3.5-fold production increase was obtained when
`compared to offset vertical wells.
`
`Nomenclature
`
`b
`
`= fracture width, ft
`
`CFd = dimensionless fracture conductivity
`
`h
`
`k
`
`= formation thickness, ft
`= formation permeability, md
`= fracture permeability, md
`= fracture half-length, ft
`r
`= weilbore radius, ft
`(Sch)c= radial convergence skin factor
`a
`= vertical stress
`
`•
`
`•
`
`= maximum horizontal stress
`
`= minimum horizontal stress
`
`Acknowledgments
`
`The authors thank the management of Choctaw II Oil
`and Gas, Ltd., Pennzoil, and Halliburton Energy
`Services for permission to publish this paper.
`
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`• "Nonplanar Fracture Propagation from a Horizontal
`Wellbore: Experimental Study," paper SPE 24823
`presented at the 1992 SPE Annual Technical
`Conference and Exhibition, Washington, DC,
`October 4-7.
`
`2. Soliman, M. Y., Hunt, J. L., and El Rabaa, W.:
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`(August 1990), 966-973.
`3. Austin, C. E., Rose, R. E., and Schuh, F. J.: "Si-
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`Treatments of Horizontally Drilled Wells," paper
`SPE 18263 presented at the 1988 SPE Annual
`Technical Conference and Exhibition, Houston,
`TX, October 2-5.
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`at the 1988 SPE Annual Technical Conference and
`Exhibition, Houston, TX, October 2-5.
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`paper SPE 25058 presented at the 1992 European
`Petroleum Conference, Cannes, France, Nov. 16-
`18.
`
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`SPE Annual Technical Conference and Exhibition,
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`
`8. Economides, M. J., McLennan, J. D., Brown, and
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`Canadian SPE/CIM/CANMET International
`Conference on Recent Advances in Horizontal Well
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`
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