SPE 106058
`
`Enhanced Fracture Entry Friction Analysis of the Rate Step-Down Test
`Leon V Massaras, SPE, Synergy Technology Co., and Alexanndru Dragomir, SPE, and Daniel Chiriac, SPE, PETROM
`
`Copyrig/112007. Society or Petroleum Engineers Inc
`
`This paper was prepared ror presenlation at the 2007 SPE Hyelrauhc Fractunng T ecllnOlogy
`Conference held ,n COiiege Station. Tel<8s U $A , 29-31 January 2007
`
`This paper was selected for p(esentat,on by an SPE Program Committee fotow1ng review of
`informabon contained in an abstract submitted by the author(s) Contents of the paper as
`presented ha\18 nol been reviewed by the Soeiety of Petroleum Engineers and are subJecl to
`correction by the author(s) The matenal. as presented, does not necessarily reflect any posit,on of
`the Soc,ety of Petroleum Engineers us officers. or members Papers presenle d al SPE meebngs
`are subject lo publication review by Edilofiat Committees of the Soaely of Petr01eum Engineers.
`Electronic reproduction d,sllibuhon or storage of any pan of this paper 10f commero-al purposes
`w1thoul the wriUen consent of the Soe1ety of Petroleum Engneers Is prohiOtec:a Pennss1on to
`reproduce in print is restricted to an abstract of not more than JOO words .Custrations may not be
`copied The abWact must contain conspicuous acl<now1edgmeo1 01 whete al'ld by whom the paper
`was presenled. Wrile Librarian. SPE PO Box 833836. Richardson. TX 750a3-3836 U S.A
`fax
`01-972-952-9435
`
`Abstract
`
`The procedures of the Rate Step-down Test (RST) also referred
`to as ''Slep-Down Test" (SDT). and of Conventional Fracture
`Entry Friction (FEF) Analysis have been used worldwide for
`over 15 years to separate the Measured Tolal System Friction
`(MTSF) into constituent components. The magnitude of the FEF
`components has served as guidance to design and/or modify the
`placement procedure and treatment schedule, in order to reduce
`unplanned
`terminations (screenouts) of propped hydrofrac
`treatments.
`Conventional FEF Analysis has inherent limitations which
`produce non-unique (somewhat erroneous) results that can only
`be overcome with Enhanced FEF Analysis methodology; which
`bypasses
`these
`limitations with
`innovative methods:
`appropriately corrected
`fluid friction
`factors, non-uniform
`perforation discharge coefficient. application of Maximum Drag
`Reduction (MDR) asymp101e, and, matching of MTSF with
`Calculated Total System Friction (CTSF) al all rates of 1he RST.
`Several RST examples are analyzed wi1h FEF .-lnafy=er to
`illustrate and document the success in placing safe and effective
`propped hydrofrac treatments.
`Real-world analogies are used as visual aids to explain the
`complex processes of FEF, along with RST design methodology,
`RST execution procedure, and detailed calculation procedures
`for performing Enhanced FEF Analysis.
`Net-pressure history matching is significantly improved, due
`to the increased accuracy of calculating the magnitudes of the
`wellbore friction and of the FEF components.
`
`Introduction
`
`FFF is the most serious impediment to placing safe and effective
`propped hydraulic
`fracture
`treatments. The
`advent and
`widespread use of the RST, along with application of
`conventional FEF Analysis methodology reduced the abnormally
`high percentage of screenouts prevalent since the inception of
`hydraulic fracturing technology in 1947.
`The major limitations of conventional FEF Analysis have
`been: over or under estimating bo1h the MTSF and lhe CTSF,
`and, difficulty in achieving a unique (correct) solution. These
`limitations result from: I) limited ability to separate well bore
`friction from perforation friction, 2) application of incorrect
`correction to fluid friction factors, 3) absence of plotting and
`matching feature to compare MTSF with CTSF, 4) ignoring the
`effect of restriction(s) in the flow path.
`FEF continues to adversely affect the safe and effective
`placement of propped hydraulic fracturing treatments in some
`regions of the world, a condition which can be improved with
`Enhanced FEF Analysis, which provides unique (correct) results
`by: I) correctly extrapolating fluid friction data for a given
`conduit diameter to various conduit diameters, 2) applying
`correct corrections 10 the fluid friction factors, 3) correctly
`calculating friction in the perforations (by applying non-uniform
`perforation Discharge Coefficient) and in the near-wellbore
`region, 4) accounting for pressure losses due to restrictions in the
`flow path, 5) applying Maximum Drag Reduction (MDR)
`methods for improved prediction of friction factors for turbulent
`flow, 6) matching of MTSF 10 CTSF at all flow rates of the
`RST. 7) accurately separating MTSF inlo wellbore friction and
`FEF, and, 8) accurately separating FEF into perforation friction
`and near-wellbore (NWB) friction
`Computer analyzed case studies are presented, which
`illustrate:
`I) the correct procedure for
`the RST, 2) the
`methodology of Enhanced FEF Analysis 3) the high level of
`accuracy possible, and, 4) how to increase the percentage
`propped hydrofrac treatments that can be placed safely and
`effectively.
`The accuracy achieved with Enhanced FEF analysis greatly
`improves Net-pressure history-matching: matching of the
`Observed Net Pressure (ONP) with the Model Net Pressure
`
`IWS EXHIBIT 1059
`
`EX_1059_001
`
`

`

`2
`
`Leon V. Massaras, Alexanndru Dragomir, Daniel Chiriac
`
`SPE 106058
`
`(MNP). This improves: I) the on-site decision-making process,
`2) helps to safely place optimum, and effective propped
`hydrofrac treatments. and 3) increases the assets with which one
`operates (reduces risk).
`
`Venturi Flow Meter Analogous the Wellbore-Fracture
`System
`
`The Venturi Flow Meter (VFM) is a measurement instrument
`which is analogous to the wellbore-fracture system. It is used
`extensively in the water supply and other industries. In the
`petroleum industry the VFM is used in surface well testing
`equipment, subsea wellhead installations, and, as a bottomhole
`flow meter in "intelligent',' well completions.
`
`A web-based "hands-on" exercise with an animated VFM can
`be accessed by clicking at the link in ref. 21.
`
`Stagnation Pressure
`
`In a VFM the fluid continues flowing downstream, whereas, in a
`perforation/small-fracture system the fluid loses velocity and is
`forced to reverse direction. as shown in Figure 3. This pressure
`behavior is similar to that occurring in a VFM, as previously
`discussed.
`The combination of flow reversal and velocity decrease
`create high pressure inside the small fracture, which is referred to
`as stagnation pressure, and which causes fracture initiation and
`propagation.
`
`llomounl Equation
`x• n&ationshlP
`
`-a l Eqwllon
`JC1 rwLltiQM.hlp
`
`- I l l Equation
`X1 ,elitionst,ip
`
`Figure 1: Standard VFM, showing velocity and pressure relationship,
`
`and that velocity Is a function of flowrate squared, Q 2, for all sectors.
`(Adapted and modlfled from ref. 1).
`
`Figure I shows a standard VFM configuration. The fluid
`velocity, V2, in the narrow section (throat) is much higher than
`the fluid velocities upstream, VI, or downstream, V3. The
`velocity increase in the throat causes the pressure to decrease,
`due to conservation of energy. All sections (upstream, throat, and
`downstream) have circular cross section, thus, the Bernoulli
`equation (a flowrate squared, Q1
`, relationship)
`is used for
`mathematical analysis of all sections.
`
`llem...UI Equation
`X' tfl41tl0t\ah1p
`
`8eMOUIU EquatJon
`,C .. rtJltion,tup
`
`F-bo-ntwo ... tos
`x" relalll;Nlt hip
`
`Figure 2: Conceptual VFM, showing velocity and pressure
`relationship and that velocity Is function of square root of flowrate,
`Q112
`, for the downstream sector. (Adapted and modified from ref. 1).
`
`A conceptual VFM, whose downstream section is shaped like
`a parallelogram (rather that a tube) is shown in Figure 2. This
`configuration would exhibit pressure drop behavior analogous to
`a Wellbore-Perforation-Fracture System, thus, the equation for
`flow between two plates (a square root of flowrate, o •·i,
`relationship) would be used for mathematical analysis of this
`section. It should be noted that if the width between the plates
`remains fixed, the pressure drop is a linear function of flowrate
`(not a function of the square root of flowrate).
`
`Figure 3: Perforation and fracture showing the velocity and
`pressure relationships, a combination of which causes high
`stagnation pressure.
`
`During the flowrate reductions of the RST the high stagnation
`pressure decreases sharply very rapidly. Thus, FEF can be
`detected and measured only with an RST. Sharp rapid pressure
`changes in the fracture .£!.!!!!2! be detected with a rate Step-Up
`Test (SUT), used to obtain other useful information.
`
`Conventional vs. True Net Pressure
`
`Prior to 1990 the ONP was conventionally calculated as per
`following equation\ and as shown in Figure 4.
`
`P11f/(OOflV) = Pm·g] • Pei ... . ......... . . ...... (I);
`
`Where, P m·g2 = (Phi,• Fcp) 1 2,
`P1,1, Bottom hole pressure "' Ps, + P1, • F,,,,,
`Fcp = Calculated Perforation Friction
`P$, "" Surface Treating Pressure
`P1, "' Hydrostatic Pressure
`F,,,11.-:: Measured Wellbore Friction
`(includes local loses)
`Pc1=Closure Pressure
`
`''Conventional" ONP to
`to as
`This will be referred
`differentiate it from the "true" ONP (subsequently discussed). In
`Equation I it is assumed that the pressure at the tip of the fracture
`is zero (0), as such, the pressure loss in the fracture, due to
`
`IWS EXHIBIT 1059
`
`EX_1059_002
`
`

`

`SPE 106058
`
`3
`
`friction is assumed to decrease linearly as a function of fracture
`length. Such a large pressure loss due to friction isn't possible,
`because, the fluid velocity in the far-field fracture is very low
`(approximately 2 ft/min or 0.65 m/min).
`Equation I doesn't account for NWB friction, because, prior
`to 1990 it was thought that NWB friction occurs only in deviated
`or horizontal wellbores. The advent of the RST and Conventional
`FEF Analysis made quantification of FEF components easy,
`which. when considered in conjunction with fracture tip effects
`(Dilatancy) made Net- pressure history matching possible.
`Calculating "true" ONP (as per equation 2), and as shown in
`Figure 4, has greatly improved Net-pressure history matching.
`
`P11e1(1ruc) - Pm-g/ - Pc1
`
`..... , ............. ........... (2);
`
`Where,
`Pm·g I PM - FEF
`Pb!, = Bottom hole pressure = Ps, + P1, - F111w
`P51 - Surface Treating Pressure
`P11 = Hydrostatic Pressure
`Fmu· Measured Wellbore Friction
`(includes local loses)
`F£F = Fracture Entry Friction = Fmp + Fmmr
`F111p Measured Perforation Friction
`F,,,111,. = Near-wellbore Friction
`Pei Closure Pressure
`
`frK1u<tPotl(cid:173)
`fud~Zone
`
`!
`I
`
`-... -
`
`Oifecuon of frac.tu,e Gtowth
`
`Figure 4: Graphic representation of FEF Components: Pressure as a
`length, Calculation of Net-pressure, and,
`function of fracture
`Fracture tip Effects jOllatancy). (Adopted and modified from ref. 9).
`
`The ONP is easy to calculate from the recorded pressure data.
`However, in order to obtain a Net pressure history match, a 3D
`fracture propagation simulator is required. Real-time monitoring,
`recording, and analysis features are a distinct advantage, as the
`"true'' ONP can be calculated while the treatment is in progress,
`It enables the engineer on-site to monitor and determine if the
`treatment is being placed as per design (safely and effectively),
`and, to be able to re-design the treatment in real-time if required.
`Older 2D fracture propagation simulators have limitations; I)
`underestimate the ONP, thus. a Net-pressure history match is not
`possible, 2) lack real-time monitoring and analysis capabilities,
`thus, real-time decision making is not possible.
`
`Fluid Lag and Fracture Tip Dilatancy
`
`For a complete understanding of the complex processes of
`hydraulic fracturing, one needs to understand and analyze not
`only what happens at the Fracture Entry (the subject of this
`paper), but also what happens at the tip of the fracture.
`There seems to be agreement on the fact that large stress and
`large pressure
`loss occur at
`the
`fracture
`tip. There
`is
`disagreement as to the analysis methodology. Several theories
`have been presented3• 4
`: I) Dilatancy at the fracture tip (non(cid:173)
`linear expansion of rock due to fluid lag), 2) Apparent Fracture
`Toughness, 3) Process zone, and 4) Continuum Damage
`Mechanics 4 (CDM). Only Dilatancy at the fracture tip will be
`discussed to some detail. The reader is referred to the many
`publications on these subjects.
`The tip of the fracture being created normally propagates
`through the formation much faster than the leading edge of the
`fracturing fluid, as shown in Figure 4. This means that the
`created fracture (fluid lag zone, ahead of the fluid) which has
`been propped open by the fluid is momentarily in vacuum and
`remains open for a very short time interval. The high overburden
`pressure dilates the rock (expands it non-linearly), and causes the
`fracture tip zone to re-close.
`When the leading edge of the fracturing fluid arrives at the
`closed region ( at the tip of the fracture). a large pressure is
`needed to re-open the fracture, as shown in Figure 4.
`The Net-pressure in the dilatancy zone can be negative
`during a short time interval as a momentary vacuum is created
`and positive when the fluid arrives and fracture reopening
`occurs. See Figure 4. To achieve fracture propagation the Net(cid:173)
`pressure in the rest of the fracture must be much higher.
`Referring to Figure 4, one would note that: I) large friction
`pressure loss occurs at the perforations and the near-wellbore
`area, 2) small amount of friction pressure loss occurs along the
`length of the main fracture (due to the very low velocity of the
`fluid in the fracture). 3) large pressure drop occurs at the tip of
`the fracture; therefore, the high pressure loss noted at the tip of
`the fracture can only be expended to re-open the closed fracture
`tip region.
`Warpinski5
`, has conducted in-situ measurements (in deep
`underground caverns) focusing on fracture propagation. The
`results from these tests tend to support the Dilatancy theory for
`fracture mechanics at the tip of the fracture.
`Another way to look at fracture tip dilatancy is to note that
`the stress intensity factor consists of a positive component from
`the positive net pressure in the fracture body, and a negative
`component from the negative net pressure in the fluid lag zone
`(Dilatancy Zone), as shown in Figure 4. The contribution of
`stress from the fluid lag zone, to the stress intensity factor, is
`much larger than the contribution from the "'main" fracture. The
`absolute value of these two components is about the same,
`however, when the fracture has propagated some distance
`beyond the wellbore area, it is much larger than the fracture
`toughness. As such, fracture toughness is unimportant when the
`fracture is fairly large. This is evident from the following
`equation for calculating Net-pressure in a radial fracture:
`
`IWS EXHIBIT 1059
`
`EX_1059_003
`
`

`

`4
`
`SPE 106058
`
`p,,., = K1/ ,J;;; ............................................. (J):
`
`with a single power law equation:
`
`Where,
`Ktc = Mode I fracture toughness critical
`stress intensity factor. (psilin° 5
`)
`radial distance to the fracture tip (in).
`
`a
`
`Since the radial distance term. "· is in the denominator, the
`magnitude of the Net-pressure required to propagate a small
`fracture
`is large, while the magnitude of the Net-pressure
`required to propagate a large fracture is small, as shown in the
`following table.
`
`KIC
`(psi!in°·5J
`
`1,000
`1,000
`1,000
`
`Radial distance
`to fracture tip
`
`Net Pressure,
`Pnet
`
`(ft)
`0.083
`12
`100
`
`(in)
`1
`144
`1200
`
`(psi)
`565.0
`47.0
`16.3
`
`(bar)
`38.9
`3.2
`1.1
`
`Since it takes veiy little Net-pressure to pro pagate a fracture.
`it follows that the high Net-pressure (noted in field operations)
`would be expended to reopen the fracture at the fluid lag zone
`(Dilatancy Zone) rather than to propagate it.
`Fracture toughness plays an important role during fracture
`initiation, because, the magnitude of the Net-pressure is usually
`large. Fracture toughness plays a minor role during fracture
`propagation. The reason for this difference is the assumption that
`the pressure in the fracture is fairly uniform all along the fracture
`length. as shown in Figure 4.
`
`Rate Step-Down Test (RST) Procedure
`
`Cleary, et al.6 were the first to propose a RST procedure, which
`consisted of abrupt and closely spaced flowrate reductions (as
`opposed to a single flow rate reduction or widely spaced flowrate
`reductions). and the analysis methodology which separates the
`friction pressure
`losses
`into the various components that
`comprise the .\ITSF, which is calculated by taking the difference
`between Surface Treating Pressure, Psr, and the Instantaneous
`Shut-in Pressure (/SIP), as shown in Figure 9.
`inexpensive to
`An RST procedure is veiy simple and
`perform. The injection flow rate is reduced to zero in 3 to 4
`abrupt steps (preferably 4 steps). The durations of the flow rate
`reductions are about equal and long enough for the injection
`flowrate and pressure to stabilize, usually 10-20 seconds. The
`best and easiest way to perform the procedure is to pump with 4
`pumps at about the same tlowrate and take out (shut down) one
`pump at a time. Typical RST procedures are shown in Figures 7.
`9, 12 and 13.
`
`Measured Total System Friction
`
`6
`
`also proposed that the plot of t.P vs. t.Q, which
`Cleary. et al.
`fits the data of the RST. represents .\ITSF, and, that the data fit
`
`,\l7SF .. K,r QP ...... ... ..... ...................... (4);
`
`Where.
`K,r= Total Friction Coefficient.
`0 - flowrate,
`P = Total Friction Power exponent.
`
`Curve fitting of the data can be performed with one of several
`techniques (least-squares, least vertical distance, etc.). If the
`measured perforation friction, F111p, dominates, the exponent P
`will be approximately equal to 2 and the plot will be concave
`friction, F,,,,,.,..
`If the Measured Near-wellbore
`upwards.
`dominates. the exponent P will be approximately equal to 0 .5 and
`the plot will be concave sideways. Note that the rounded values
`for the power exponents are used for demonstration purposes
`only.
`,\ITSF can be separated
`three constituent
`into
`The
`components and is calculated as per equation 5.
`'
`.\ITSF= F,,111 + Kp Q- + K11w Qm ..... . ............... (5);
`
`where,
`F,111.- - Measured wellbore friction,
`Q = flowrate,
`Kp = Coefficient of Perforation Friction,
`K,,... Coefficient ofNear-Wellbore Friction,
`m near wellbore friction exponent,
`(most accepted value = 0.5)
`
`The last two terms comprise Measured FEF The above
`calculations
`are
`almost
`always made
`from
`pressure
`measurements recorded at the earth surface (very near the
`wellhead valves). If the calculations are made from reflected
`(''deadstring") pressure measurements or from actual bottomhole
`pressure measurements (recorded near the perforations with
`Surface Read-Out (SRO) gauges, or, with Memoiy gauges), and
`excess pressure loss due to friction is noted, it will most likely be
`mostly near-well bore friction, no evidence of perforations.
`
`Calculated Total System Friction
`
`The CTSF is determined using various parameters: flow path
`geometiy (wellbore, perforations, near-wellbore), fluid density,
`fluid viscosity, fluid friction, etc. It is also composed of three
`components and is calculated as per equation 6.
`
`CTSI-" "' Fcw + Fcp - F rnu••·· · .. .. . . ................ (6);
`
`Where,
`Fcir - Calculated wellbore friction
`(Includes local loses),
`1-~p Calculated perforation friction,
`Fem,· = Calculated near-wellbore friction.
`
`IWS EXHIBIT 1059
`
`EX_1059_004
`
`

`

`SPE 106058
`
`5
`
`The last two terms comprise Calculated FEF:
`
`FEF = Fq> + Fc11w ...... . .. ........ . .................... . (7);
`
`Unique values of the magnitude of all friction components in
`the system will be calculated only when a match of ,\/TSF and
`CTSF (at all flow rates of the RST) has been achieved. i.e.,
`.\ITS!- -= C1Sf~ as per equation 8, and as shown in Figure 5.
`
`CTSF is not unique, as the match is made only at the highest
`injection rate. This causes incorrect allocation and distribution of
`the C1SF into the various constituent components, as shown in
`Figure 6 and in the following table.
`
`otal Sy~tem Friction (TSF) Plots
`
`Men. TSF
`~
`- - Ca!c,TSf
`
`- - - -Cale. FEF
`-i-wellbore friction
`
`100
`
`j 15
`; 50
`• .,
`I> ..
`Q. 25
`
`0
`0.00
`
`1.00
`
`2.00
`Injection rate (m'lmin)
`
`3.00
`
`4 ;0()
`
`Figure 6: Conventional FEF Analysis showing how the TSF is
`allocated Incorrectly to the various FEF Components.
`
`It is obvious from the plots of Figure 6 chat if excess well bore
`friction is subtracted, an equivalent amount will be added to FEF
`(to be able to match ,\/TSF with CTSF). This changes the shape
`of the FEF curve, making it more linear. A linear curve can
`easily be composed from an f= f (Q~) curve and an F=:f (Q1''!)
`curve because one curve is concave upwards, and the other is
`concave sideways (down). In such a case, measured FEF
`matches calculated FEF and MTSF matches CTSF. However, the
`magnitude of both FEF components would be incorrect.
`The issues outlined above are exacerbated by the difficulty to
`accurately estimate Wellbore Friction. Keck et al.7 compared
`calculated Bottomhole (BH) pressures (derived from pressure
`data recorded at the surface), with measured BH pressures
`(recorded with memory gauges). They report variance in the
`range of 30-60% in
`the magnitude of the calculated BH
`pressures.
`A summation check of results as obtained from Conventional
`FEF Analysis shows correct results, where in fact there are many
`solutions. The color coded rows correspond to the color coded
`plot lines in Figure 6.
`
`Cale.
`Near(cid:173)
`wellbore
`Friction
`bar ,
`
`Cale. Total
`System
`Friction
`bar
`
`Due to lhe trial-and-error nature of lhe analysis, it is best to
`perform the analysis with specialized software such as FEF
`.-lnaly=er, as shown in Figures 7, 9, 12 and 13.
`
`Totai System Frldlon Plots
`
`e U11as. TSF
`-----Cale. TSF
`
`■ Cllc. FEF
`Wtllbon friction
`
`~
`
`~ 200 +----+----+-----,f----+..flL'--
`-;
`..
`"' e 1so +-----+----+----t----:..-1'--+-- --.rl
`~ 100 +-- - -+------11-_,,:c--t-
`.,,
`!
`A. 60
`
`-:::::aa11f"'"'9-- --=--i
`
`0
`
`0
`
`0.5
`
`1
`U5
`Injection rate (m3/mln)
`
`2
`
`.....-.C 11 c. F EF
`
`FEF Plots
`
`_...,P,rfor.111on F r1ctlon
`__, IN . . -w1Ubore F rlct on
`
`... IMHS. FEF
`"' ~ .. 60
`:i .,, ... 40
`
`100
`
`~ 80
`
`!
`A.
`
`20
`
`0
`
`0
`
`0.5
`
`1.5
`Injection rate (m1lmin)
`
`2
`
`15
`
`Figure 5: Plots of MTSF matched with CTSF, and, of Measured FEF
`matched with Calculated FEF.
`
`Conventional FEF Analysis of the RST
`
`Conventional FEF Analysis of the RST utilizes regression
`analysis and a dual curve-fitting technique to separate and
`quantify the two FEF components. The match of .\ITSF with
`
`IWS EXHIBIT 1059
`
`EX_1059_005
`
`

`

`6
`
`SPE 106058
`
`Enhanced FEF Analysis of the RST
`
`Enhanced FEF analysis of the RST calculates unique
`(accurate) values for the magnitude of the two FEF componen1s.
`FEF .-lnaly=er can easily accomplish this, as shown in Figures 7.
`9, 12 and 13. All known constants are input first, followed by
`input of the variables. A trial-and-error procedure is required
`because of the unknown variables.
`Many variables can be changed; however, to simplify the
`solution procedure only three variables are normally varied until
`a solution is obtained. These variables are: Fluid Friction
`Coefficient, Number of open perforations, and, Coefficient of
`NWB Friction (Tortuosity Coeff.). Solution is reached when the
`plot of the ,\ITSF matches the plot of the CTSF, at all flow rates
`(not just at the maximum flow rate).
`The magnitudes of most of the terms of the CTSF are
`calculated using equations and algorithms found in standard
`Petroleum Engineering and Fluid Mechanics textbooks. Detailed
`calculation procedures are presented
`in
`the appendices as
`follows:
`
`Aonendix Calculation Procedure
`A
`Wellbore Friction
`B
`Perforation Friction
`Near-wellbore Friction
`C
`
`Enhanced FEF Analysis of the RST calculates very accurate
`values of all friction components because it incorporates unique
`features: I) unique capability to correct fluid friction factors
`accurately, 2) use of non-uniform perforation discharge
`coefficient, 3) accurately separating well bore from perforation
`friction (difficult because they exhibit similar concave upwards
`behavior), 4) accounting for the effect of restriction(s) in the flow
`path, 5) applying Maximum Drag Reduction
`(MOR)
`methodology, 6) Matching of MTSF to CTSF at all rates of the
`RST.
`
`~
`
`permeability reservoirs it is as high as 30%. In low permeability
`reservoirs it is as low as 1-5%.
`The above stated percentages indicate that even though the
`current RST procedure is adequate, Conventional FEF Analysis
`methodology isn't. Enhanced FEF Analysis is required to
`achieve significant improvements.
`
`Basis of FEF Analysis
`
`Energy storage considerations (in a fairly large fracture),
`preclude abrupt changes of the ONP (pressure which holds the
`fracture open). The RST takes advantage of this phenomenon. If
`an abrupt change in the calculated Net-pressure is noted. then it
`must be due to the fact that wellbore friction or one or more of
`the FEF components used for the ONP calculation is calculated
`incorrectly. The concept is illustrated in Figure 11.
`The SOT is also based on the difference in the friction
`pressure loss behavior, between the perforations, and, the
`tortuous near-wellbore area of the fracture.
`The perforation pressure loss due to friction is a function of
`the square of the flow rate f (Q\ whereas, the near-wellbore
`pressure loss due to friction in most cases (not always) is a
`function of the square-root of the flow rate f (Q'"), m'"0.5 (see
`appendix C).
`As shown in Figure 9 the difference in friction pressure loss
`behavior can be utilized for analysis in order to determine values
`for the FEF components.
`A minimum of three and preferably four abrupt flow rate
`changes are required. The duration of the "steps" must be very
`small. The subsequent sections entitled "RST Design" and "RST
`Procedure", present design reasoning, detailed procedure, and
`methodology.
`
`RST Design
`
`To correctly design an RST it is necessary to understand that the
`fracture geometry should change very little during the test. This
`avoids introduction of error(s) in the friction c alculations. A
`relatively large fluid volume should be injected prior to initiating
`the RST procedure of abrupt flow rate changes.
`The RST's plotted on the left side of Figure 8 would be
`designed improperly: the first has a small volume pumped ahead
`followed by long steps in the RST, while the second has a small
`volume pumped ahead followed by short steps in the RST.
`
`1 .. pr~ be ~
`
`lMI l>tMQM
`
`I ..
`
`J
`
`! :~::: :. ~-
`1-•
`..
`.
`~ .. ' .. :t ~--
`..
`-----
`
`t
`
`U
`
`1
`
`••
`
`•
`
`1 1
`
`Figure 7: Enhanced FEF Analysis
`
`Enhanced FEF Analys is when utilized properly can and has
`achieved significant decreases in the percentages of screened-out
`propped hydrofrac treatments. These percentages remain high in
`in medium and high
`some regions of the world. Usually.
`
`TIIM
`
`TttM
`
`Figure 8: Improperly and properly designed Rate Step-down Tests.
`(Adopted and modified from ref. 9).
`
`IWS EXHIBIT 1059
`
`EX_1059_006
`
`

`

`SPE 106058
`
`7
`
`This can be seen from the large pressure change corresponding to
`the final rate reduction.
`Upon close visual inspection of the plots, one will note that
`the change in the Near-wellbore friction plot (.1.P4) has large
`values corresponding to the last flow rate change (AQ4). and that
`the entire plot is above the Perforation Friction plot, i.e., Near(cid:173)
`wellbore friction dominates. If this situation exists. remedial
`measures can be taken to reduce near-wellbore friction.
`
`A proper RST design is shown on the right side of Figure 8.
`During
`this RST
`the fracture geometry will not change
`dramatically during the very short RST procedure. because, a
`significantly large fluid volume was injected prior to initiation of
`abrupt flow rate reductions.
`
`RST Procedure
`
`A Step-by-step procedure for the RST follows:
`I. A minimum of three and preferably four instantaneous
`flowrate reductions are required, for example: 2.4, 1.8,
`1.2, 0.6 and O m1/min. It is not required that all flowrate
`reductions be equal, however, they should be abrupt. It is
`easiest and most convenient to pump with four pumps at
`about equal rate each, and take out one pump at a time.
`The last rate reduction must be to zero m3/ min. The
`reasons for this are: a) Plots of Ap vs. AQ have O. 0 origin.
`See Figures 7, 9, 12 and 13, b) ISIP must be recorded for
`use in calculating Total System Friction, etc., and. c)
`Need to record hydraulic transient harmonic response
`(water hammer).
`2. Each step of the flow rate reductions should be about I 0-
`20 seconds long. Enough for the flow rate and pressure to
`stabilize.
`3. Fracture geometry should change very little during the
`RST. Therefore, the volume pumped prior to initiation of
`the abrupt flowrate reductions must be fairly large. See
`previous section entitled "RST Design."
`4. There should be only one fluid in the wellbore and in the
`near-wellbore region (preferably linear gel with low
`gelling agent concentration). Both density and viscosity of
`the fluid must be uniform; thus, the hydrostatic pressure
`and the wellbore friction will be constant.
`
`Most situations dictate that cross-linked fluids should not be
`in the wellbore, perforation. or near-wellbore zone during the
`RST, because, the pressure is not transmitted very well through
`the wellbore. Usually, the Fracturei'Fluid Efficiency Test (FET)
`is performed with crosslinked gel, which is overdisplaced with
`linear gel prior to performing the RST.
`
`RST Analysis and Interpretation
`
`When does Perforation Friction Dominate?
`On the left side of Figure 9 the plots show data and analysis of a
`typical RST where perforation friction is larger than (dominates)
`near-wellbore friction. This can be seen from the large pressure
`change corresponding to the initial rate reduction.
`Upon close visual inspection of the plots, one will note that
`the change in perforation friction (API) plot has large values
`corresponding to the first flow rate change (AQ I), and that the
`entire plot
`is above the Near-wellbore Friction plot, i.e.,
`Perforation friction dominates. If this situation exists, remedial
`measures can be taken to reduce perforation friction.
`
`When Does Near-wellbore Friction Dominate?
`The plots on the right side of Figure 9 show data and analysis of
`a typical RST case where wellbore friction is larger than
`(dominates) perforation friction.
`
`...
`
`. ,..
`
`~ ·
`
`'t4
`
`'"'Ill
`
`•
`
`.02
`I
`
`I
`
`_ _ .,..
`
`4 •J
`
`IOII'
`
`"
`
`-: ,
`
`,.~
`
`~~
`
`~~ ~~
`
`~ z
`
`~~
`
`~~
`
`.-._c.._-,.,
`
`""' , , ...
`I
`""' I J. - 1
`; ... ~ .
`........ .,
`~,.,.... ....... ,.....,
`, ..
`... ............. ,__
`I. ~-
`l ,. f ._ ___ ~ , --
`1-
`
`"°'
`
`401 ',
`"°'
`
`1
`
`"1 - -
`
`..
`..
`
`~~ ~~
`
`~ ~
`
`j J.
`'
`r .. 1...,._ _....__.__
`
`~~
`
`_ ............. ,.,.._
`
`~, .........
`
`..
`........ ... _._,.
`
`-
`
`Figure 9: Plots on the left show that perforation friction dominates,
`while plots on the right show that near-wellbore friction dominates.
`(Adopted and modified from ref. 8 and 91,
`
`Memory Device (Mnemonic)
`
`An easy way to determine which FEF Component is larger is to
`note that the fluid goes through the perforations first and through
`the near-wellbore zone last (second). So, if the first pressure
`change is larger than the last pressure change, you have more
`perforation friction.
`By the same logic, the fluid goes through the near-wellbore
`area last (second). So, if the last pressure change is larger than
`the first pressure changes, you have more near-wellbore friction.
`It should be noted, that in the event wellbore friction
`dominates. it can "mask" the FEF signature (it won't be reflected
`clearly in the surface pressure drop). Thus, it can be difficult to
`ascertain which FEF component dominates.
`
`Abrupt Changes in ONP Not Possible
`
`Energy storage considerations dictate that it isn't possible to have
`abrupt changes in the ONP. This fact can be used to determine if
`the ONP is calculated correctly, i.e., if the correct friction values
`for wellbore friction or for the NWB friction
`are used
`components.
`The procedure is very simple. A flow rate reduction or a very
`short shut-in is performed. See Figure 11. If an a