DFIT - Diagnostic Fracture Injection Test
Applications of Mini FracsDFIT - Diagnostic Fracture Injection TestBy: Saad Ibrahim, P. Eng.For information:www.petromgt.com2015Petro Management GroupQuality Petroleum Engineering ConsultantsServices: Reservoir Studies (Conventional/Simulation) Well Test Planning and Analysis Waterflood Design & Performance Monitoring Production Optimization Performance Evaluation of MFHW’s (PTA, RTA, Numerical) Reserves and Economic Evaluations Complete frac design/optimization (Gohfer/KAPPA software) Government Submissions Customized course contents Expert Witness
Petro Management Group - FracKnowledgeFull Well Frac Design and Optimization Services:Geological Mineral contents Natural fractures Core/Sweet spotsGeologicalDataGeo-mechanical Poisson’s ratio Young’s modulus Brittleness IndexReservoir Eng. DFIT and PTA RTA Reservoir tyOptimum FracDesignComplimentary lunch and Learn Seminars Challenges of Reserves Estimate for tight and unconventionalreservoirs - (Feb. 24) Waterflood Application for MFHW’s - (March 25) Applications of Mini Frac (DFIT) - (May 7th) Performance Evaluation of Multi-Stage fracs Hz Wells(MFHW’s) - (June 18) How to get the Most out of Well Testing Frac Databases: benefits to improve frac results How can we improve your frac design/performance in thispoor oil price environment
Industry and In-house Training Courses Fundamentals of Reservoir Engineering Well Test Analysis Workshop Performance Evaluation of Horizontal Wells Waterflood Management Enhanced Oil Recovery Petroleum Engineering for Non-EngineersBenefits of in-house training: Up to 60% discount off the industry standard fees Customization ConfidentialityApplications of Mini FracsDFIT - Diagnostic Fracture Injection TestAgenda: Introduction Applications/benefits Types of DFIT analyses Pre-Frac Closure After Closure Analysis (ACA) Case study (Duvernay Shale Gas) Case study from Haynesville shale gas
Why Conduct a Mini Frac Test? Estimate reservoir parameters needed for frac design Formation permeability Reservoir Pressure Other reservoir parameters (fluid leakoff, natural fractures) Environmental reasons; determine ceiling injection pressureof the cap rock for (AER requirement) for: Steam-flooding projects Water disposal/injection projects Optimize water/fluid injection in EOR schemes Avoid over-injection (over the frac pressure) Avoid under-injection (much lower than the frac pressure) Optimize drawdown during flowback to avoid frac damageMini Frac TestTight formations:Inj rate: 1-7 Bbl/mininj vol: 20-50 BblCap Rock (Clearwater):Inj rate: 2 to 150 L/minInj vol. 7 m 3Fracture connects the formation with wellbore;past the damaged zone Short injection test (5 to 15 min.), followed by a few hrs of fall-off period Formation is broken down to allow wellbore/formation communication pastthe damaged zone No proppant is used Specialized low-rate injection pump, with automated flow rate control bymeans of a DCS (Digital Control System) Provides better results than closed chamber tests
Information Obtained from DFIT Obtain information critical to frac design: Fracture Propagation PressureInstantaneous Shut-in Pressure (ISIP)Fracture Gradient (ISIP/depth)Fracture Closure pressure (FCP)Identify leakoff mechanism - leakoff coefficient Identify flow regimes, to confirm reservoir parameters: Reservoir pore pressure Formation flow capacity/mobility and Permeability Net Fracture Pressure (NFP) Fracture complexity Fracture progress/monitoring Well flowback planning Determine completion efficiency (step-down rate test) Pressure drop in perforation Pressure drop as a result of well tortuosityLimitations of DFIT Performed under injection conditions. Permeability will tend tobe slightly higher than under drawdown conditions (stresssensitive permeability). Short tests will provide upper bound for pore pressure Low pressure reservoirs problematic for surface pressuremonitoring; would require bottomhole shut-in and gauges
Fracture Orientation is Controlled byIn- Situ Stress Field 7 677 66 Vertical fracture Where:σ1 σ2 σ3 σ1 : Overburden stress σ2 : Principle (max. stress) σ3 : Minimum stress (closure stress)Fracture Orientation is Controlled byIn- Situ Stress FieldHorizontal fractureWhere:σ1 σ2 σ3Shallow Depth 1000 ft σ1 : Principle (max) horizontal stress σ2 : Minimum horizontal stress σ3 : Overburden pressure (Lowest stress)
How to Determine Stress Direction?FMI logFracture MicroImage LogCalliper logsWorld Stress Map
Why Minimum Stress ( σ3) is Important to Know?ProppantembedmentFluid residueDamaged zoneFiltercakeProppant collapse Where: σ1 : Overburden stress σ2 : Principle (max. stress) σ3 : Minimum stress (closure stress)Mini Frac Typical Pressure ProfileRule:Pf ISIP PcBreakdownPressureFracturePropagationPressure PfInstantaneousShut-inPressure or ISIPInjectionFracture ClosurePressure or FCPNo flowback testPseudoLinear FlowPseudo RadialFlowFractureDominatedReservoirDominatedISIP: the minimum pressure required to hold open a fracture
Fracture Dominated AnalysisQISIP: identified by significant Slope ChangeDetermination of ISIPISIP Gc . mG PcWhere:ISIP:Pc:Gc:mG:Instantaneous shut-in pressureClosure pressureValue of the G-Function at closure pressureSlope of the G-Function prior to closure pressure
What is G-Function?G-function is an analytical technique used to define the closurepressure and the types of leak-offG t D 4 g t D g 0 4 1 t D 1.5 t D 1.5 for 13 0 .50 .5g t D 1 t D sin 1 1 t D t Dg t D for 0.5 t D t t p t pG-function is a dimensionless function of shut-in time normalized topumping timeBy: Kenneth G. Nolte in 1979Pre-Closure AnalysisThe G-Function is used to determine the Fracture ClosurePressure (FCP), and identify the common leakoff types: Normal Leakoff Pressure dependent Leakoff Fracture Tip Extension Leakoff Fracture Height Recession Leakoff
Normal LeakoffWhen does it occur?PressureFirst derivativeG- derivativeOccurs when the fracturearea is constant during shutin and the leakoff occursthrough a homogeneousrock matrixPcFracture closureGc0Characteristics:12348 Pressure derivative (dP/dG) during fracture closure (first derivative) The G-Function derivative (G dP/dG) lies on a straight that passes throughthe origin (G-Function derivative) or semi-log derivative Deviation of G-Function from the straight line, determines fracture closurepressure (FCP)Frac (fluid) Efficiency (ή)Frac (fluid) Efficiency (ή) Total fluids injected - Fluid LeakoffTotal fluids injected Fluids remaining in fracTotal fluids injectedA high fluid efficiency means low leakoff and indicates the energy used toinject the fluid was efficiently utilized in creating and growing the fracture.Unfortunately, low leakoff is also an indication of low permeability.High leakoff (high fluid loss)Low leakoff (low fluid loss)InvadedZonePossible screen-out
Frac (fluid) Efficiency (ή)(ή) Gc G c 2 For Gc 3ή 3/(3 2) For Gc 30ή 30/(30 2) 94% 60%at closure pressureHigh leakoff or high fluid lossLow leakoff or low fluid lossWhere:Gc: is the G-function time at fracture closurePressure Dependent Leakoff (PDL)Naturalfractures
Pressure Dependent Leakoff (PDL)When does it occur?When secondaryfractures existent in theformation and intersectthe main fractureCharacteristics:PressureFirst derivativeG- derivativePcGc G-Function shows a large hump above the straight line Subsequent to the hump, G-Function shows a normal leak off(linear trend) The end of the hump identifies the fissure opening pressure Deviation of G-Function from the straight line, determines fractureclosure pressure (FCP)Fracture Tip Extension LeakoffWhen does it occur?PressureFirst derivativeG- derivativeOccurs when a fracture continues togrow even after injection is stopped andthe well is shut-in. It is a phenomenonthat occurs in very low permeabilityreservoirs, as the energy which normallywould be released through leakoff istransferred to the ends of the fractureresulting in fracture tip extension.Characteristics:G-Function The G-Function derivative G dP/dG initially exhibits a large positive slope thatcontinues to decrease with shut-in time, yielding a concave-down curvature. Any straight line fit through the G-Function derivative G dP/dG intersects the y-axisabove the origin.As long as the G-Function keeps increasing, fracture closure hasNOT occurred yet
Mini Frac Followed by a Flowback PeriodWhy a flowback after mini frac is needed? For a “fracture tip extension” leak-off, fracture closure is notobserved. Therefore, a closure pressure can’t be estimated An excessively long fall-off period is required to observefracture closure Flowing back the well after the fall-off period, will inducefracture closure; and hence, allow an estimate of theclosure pressure (Pc).Mini Frac Typical Pressure Profile(with Pi Fracture initiation pressure (leak-off)Pb Fracture break-down pressureFPP Fracture propagation pressurePC Closure pressure during fall-offP*C Closure pressure during flow P Draw-down pressure during flowback
Considerations for the FlowbackIn order to clearly observe the closure pressure, it isrecommended to select the flowback rate at approximately 1/6to 1/4 of the last injection rate.Fall-offFlowbackPcCorrect RateRate too highTimeRef: Nolte K.G “Fracture Evaluation Using Pressure Diagnoses”Fracture Height Recession LeakoffWhen does it occur?Occurs if the fracturepropagates throughadjoining impermeablelayers during injectionPressureFirst derivativeG- derivativePcGcCharacteristics: The G-Function derivative G dP/dG lies below the straight lineextrapolated through the normal leakoff data. Both G-Function and the first derivative exhibits a concave up trend
Use of Square Root of Time ( t ) to Pickthe Closure Pressure (Pc) ?213 (correct Pc)465shut - in timeShut in Time2007 SPE Hydraulic Fracturing Conference in College Station, Texas,.by: Ken NolteUse of Square-root of Shut-inTime Plotto Confirm Closure Pressure (Pc)dPd t(correct Pc)dPtd ttFirst derivativedPvs.d ttG-Function orSemi-log derivativetdPvs. td tClosure pressure is recognized by a “local” high on the First Derivative plot
After Closure Analysis (ACA)Reservoir Dominated Analysis:Fracture ClosurePressurePseudo Linear FlowPseudo Radial FlowAfter-Closure Analysis, from Talley et al (SPE 52220)Log-Log Diagnostic Plot(Normal Leak-off)Log-Log Plot100001000ClosurePressureSlope 1Wellbore storage100 P t .100.0010.010.1 t, hrs1.010.0d( P)d( t)100Closure pressure; determined from the G-function and t plots,occurs also when the derivative plot deviates from the ½ unit slopestraight line on this Diagnostic plot
Flow Regime Diagnoses After ClosureUse of the pressure diagnostic Log-Log plotDefinition of Pressure Derivative Plots(DFIT Analysis)For very short injection/production period relative to the falloff/buildup period:Use “injection/drawdown” derivative:The derivative plot is the slope in a plot of pressure versuslog t, from the semi-log plotFor reasonable injection/production period relative to the falloff/buildup period:Use “fall-off/buildup” derivative:The derivative plot is the slope in a plot of pressure versuslog (tp t)/ t, from the semi-log plot
Method of DeterminingFracture Closure Pressure (FCP)1. G-Function Plot2. Square Root Plot3. Log-log Diagnostic PlotNet Fracture Pressure (NFP) vs. FractureNetwork ComplexityFracture Extension ModelSimpleOff-balanceComplexThe more complex the formation, the more natural fracturesmay exist and the higher is the Net Fracture PressureRef: Dan Potocki, SPE 162814
Net Fracture Pressure (NFP) vs. FractureNetwork reNFPISIP OBclosureMore Induced Fracture ComplexityIncreasing NFPSchematic of Net Fracture Pressure (NFP)Indicating Progress of Fracture ted ExtensionlVLog of TimeI - Confined height; unrestricted ExtensionII - Constant NFP plateau can result in unstable growth, fluid loss or fissures openinglll - Fracture growth ceases.continued injection increases width of the fracture; ballooneffect. This is the desired behaviour if a tip screenout treatment has been designedlV - Unstable height. During fracturing, if a barrier is crossed and encountered a lowerstress zone (Pf σzone) an accelerated height growth will occur, which is undesirable should terminate injectionSource: Nolte, K.G. and Smith, M.G. 1981. Interpretation of Fracturing Pressures. J Pet Technol 33
After Closure Analysis (ACA)Procedures:1. Flow regime diagnostic Plot:a. Confirm flow regimes (radial, linear)b. Estimate reservoir pressure, PRPPt2. Radial flow analysis Pa. Confirm reservoir pressure, PRb. Estimate formation permeability, k tAfter Closure Analysis (ACA)1. Flow regime diagnostic Plot:Fall-off data is plotted on a Log-log of dP vs the square of thetime function “FL”: P: (Pt - PR) Time function (FL)FL Where:- FL :- Pt :- PR :- Tc :2 . sin 1tctdimensionless time functionPressure at shut-in “t”Static/stabilized reservoir pressureTime at fracture closure pressureValid only for t tcPR
Flow Regime DiagnosesProcedure: The analysis depends on an accurate closure pressure pick;to use after closure data (t tc) The pressure difference ( P) or (Pt - PR) curve is completelydependent on the value of reservoir pore pressure used(estimated) The pressure derivative is insensitive to the reservoirpressure estimate For this reason the method is iterative and the pressurederivative should be used for all initial analyses.After Closure Analysis (ACA)Identification of Radial Flow RegimeP- Pi(FL2).d(P-Pi)/d(FL2)Start radial flow1000Start of radialflow1001E-41E-30.010.1Square Linear Flow (FL2)1Radial flow is confirmed when both dP and pressure derivativecurves overlap, forming a straight line with a unit slope
After Closure Analysis (ACA)2. Radial flow analysis:Fall-off data is plotted against the time function “FR”: Fall-off pressure data vs. Time function (FR)FR x . tc 1. ln 1 4 1 tc Where:x 16 2 1.6After Closure Analysis (ACA)Radial Flow Analysis Vi 251,000 MR . t c kh11800 116001140011200PRStart of radialflow1100000.020.040.060.080.10.12Radial Flow (FR) Extrapolation of the straight line of the radial flow regime, yields thereservoir pressure (PR) The slope of the line (MR), yields the flow transmissibility (kh/μ)
Permeability Est. from G-FunctionThis empirical formula gives an estimate of the permeability when afterclosure radial flow data are not availablek 0.0086 f 0.01 PISIP Pc c t G c . E . rP / 0.038 1.96Where:K:μf :PISIP:Pc:N:ct:Gc:E:rP:Formation permeabilitymdFluid viscositycpInstantaneous shut-in pressurepsiClosure pressurepsiPorosityfracTotal compressibilitypsi-1G-function at closure pressureYoung’s ModulusMMpsiLeakoff height to gross frac height ratioMini Frac DesignImportant tips: It is important to obtain a rough estimate of the frac pressureprior to test from: The Eaton’s formula, or Knowledge from offset wells It is recommended to run BHP recorders instead of measuringWHP’s to avoid: Inaccuracies in converting WHP data to BHP In case the WHP goes on vacuum Insulate wellhead, if high ambient temperature fluctuation is expected Fill up wellbore with water before starting injection to reduceWBS duration and avoid pressure spikes (wtr. hammering) Add 3% KCI to injection water to reduce potential formationdamage
Mini Frac Design (cont.)Test duration: The lower the injection pressure, the shorter the fall-off period toreach radial flow The shorter the injection period, the shorter the fall-off period Time to radial flow regime is approx. 3 time it takes to reachclosure pressureSource: JPT September 2014How to Estimate the Fracture PressureEstimate of Fracture Pressure/GradientField :Well :Eaton’sFormulaSouth PiersonTypical WellZone :Lithology:SpearfishDol/SSuP (frac) NOB ( ----------------- ) P (PV)1- uPsi/ftWhere :P (frac) :NOB :u :P (PV) :PD :Fracture Pressure GradientNet Overburden Pressure Gradient(Overburden Grad.- Pore Pressure Grad.)Poisson's Ratio "u" 0.27 Limestone0.33 SandstonePore Pressure GradientCurrent 'Reservoir PressureDepthSummary Results:Fracture Pressure GradientFracture (Parting) PressureNote:Overburden gradient is 1.0 Psi/ft0.475 Psi/ft1606 Psi11075 KPa0.475 Psi/ft0.858 Psi/ft0.280.142 Psi/ft479 Psi3378 ft
Impact of Ambient Temperature on DFITAmbient temperature change between day & night over 50 oF(10 oC), can yield cyclic measured pressure data measured atthe surface which makes DFIT analysis difficult, and results willbe unreliable. This can happen under 3 different scenario’s: Thermal compensation of pressure recorder Thermal expansion/contraction of the fluids in the wellbore The use of capillary tubing to connect the pressure recorder to thewellhead is questionable.Source: JPT September 2014Pressure and Temperature ProfilesWHPBHPBHTWHT The cyclic change in the ambient temperature, has affected bothwellhead and bottom hole pressure data for uninsulated wellhead. No affect on bottom hole temperature
Benefits of Wellhead InsulationWHP (uninsulated)WHP (insulated)WHTThe wellhead pressure curves in a well with insulation and without insulationare shown with the fluctuation in surface temperatureBenefits of Insulating WellheadBenefits:Delta Surface PressureG dP/dG Smooth data duringradial flow Easy to recognizeclosure pressurePre-closureACARecommendations: Insulate wellhead Use fluids with lowthermal expansion toreduce cyclic pressurescaused by changes inambient temperatureACA: After closure analysisDelta Surface PressureG dP/dGPre-closureACA
Info from DFIT Used for Frac Model Input Basic reservoir parameters; perm and pressure Geological data; such as the presence of natural fracturesand geological complexity (NFP) Leakoff type and coefficient (rate of fluid loss to theformation) Frac efficiency Calibration of local stress profile obtained from open holelogsCalibration of Local stressFrac models utilize rock mechanic parameters; Poisson’s ratio andYoung’s Modulus, to generate local stress profile. Closure pressurefrom DFIT can be used to calibrate the generated stress profileClosure Pressfrom DFITNPFIncreased frac heightand lower lengthClosure Pressfrom DFITNPF
Case StudyMini FracDuvernay FormationDuvernay ExDuverny mini frac - Shortcut.lnk (Command Line)Test Raw DataReal time pressure measurement was used. Final fall-offperiod extended to 650 hrs (27 days)
Injection Period114 897 kPa !!Injection pressures are too high, reaching114.9 mPa, and injectionperiod a little long; 25 minutesDiagnoses of Flow RegimesLog-Log Diagnostic PlotStart of RadialFlow (slope -1) t, hrs Pressure derivative plot showed a straight line with a slope of -1 after only 20 hrs ofshutin. Has radial flow really been reached? Departure of derivative from ½ slope, confirms closure pressure
G-Function PlotFractureClosureG-functionFrac height recession leakoff;very high injection pressure was usedIdentification of Closure Pressure(Square Root Plot)dPd tdP / ttdPd tt . dP / d tFractureClosureSquare root of timeClosure pressure is confirmed by a “local” high of the square root plot
Identification of Radial FlowStart of RadialFlow RegimeP- PiStart radial flowRadial Flow Analysis (ACA)Start of RadialFlow RegimeRadial Flow (FR)Mobility (k/u) 0.00937K 0.00937 x 0.033 0.0003 md
Horner PlotSummary of Results
Control of Well Flow-backDesign criteria: Proppant strength (σprop), type, and concentration areselected to ensure it can withstand the local stresses in therock (Pc); otherwise it could get crushed and the fracturebecomes in-effective Increased draw-down, during the cleaning period (flow-back),can result in poor frac characteristicsEffect of Pressure Draw-down onProppant DesignProppants keep the frac aperture wide open:Pc7σpropPcWhere:66Pc7ΔP67σpropPcσprop Pc ΔPdrawdown σprop :Proppant mechanical strength Pc:Closure pressure pdrawdown: Draw-down pressure6 6
Effect of Pressure Draw-down onProppant DesignProppants are crushed; frac is closing:PcσpropPcσpropΔPPcPcσprop Pc ΔPdrawdownIf Pc is relatively high, draw-down pressure should be controlled toavoid crushing the proppants/frac closureCase StudyImpact of Well Flowback on Performance(Haynesville Shale Gas)SPE: 144425
Background T 300 to 350 oF Pressure 10,000 psi (pore pressure gradient) . 0.95 psi/ftStratigraphy
Performance ComparisonVertical Well vs. 1st Hz WellHorizontal Well & Vertical Well Production Records (Cum 7008009001000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000Time, hrsSCADA Rate24.2 Eq V. Well RateSCADA Cum24.2 Eq V. Well Cum Hz well perforation: four (4), two-foot clusters, 6 SPF, 60 degree phasing Disappointing results of first Hz well, relative to vertical wellsCritical Draw-down PressureA12200Bottom Hole Calc Pressure (psi) ACorrected Pressure (psi)AG*dP/dG (psi)E1Time BHCP CP DP FE DT17.16 11603 11559 488.1 90.14 1225ClosureE125011210012000(22.14, 1020)100011900118007501170011600500(m 46.06)1150025011400Highest Pc 11,603 psi1130011200(0.002,(Y 0) 0)5101520250G(Time)Critical draw-down pressure Closure pressure - Reservoir pressure 11,603 - 11,108 488 psiFracture could close if, during the flow-back, the wellcritical draw-down is exceeded
Draw-down Exceeded Critical LimitHorizontal Well Drawdown Estimates100,000100000qg . 22 MMscf/d10,000100001000Critical draw-downpressure . 488 12/0901/22/0902/01/0902/11/0902/21/09DateRate (MSCFD)Actual WHFP (psi)Estimated BHFP (psi)Critical Drawdown (psi)Estimated Drawdown (psi)Initial gas rate of 22 MMscf/d was maintained only for one weekDraw-down Below Critical Limit(one month of flow-back)Horizontal Well Drawdown Estimates100000100,000qg . 22 MMscf/d10,0001000Critical draw-downpressure . 488 /23/0812/28/08DateRate (MSCFD)Actual WHFP (psi)Estimated BHFP (psi)Critical Drawdown (psi)Estimated Drawdown (psi)Gas rate out-performed previous case for over a month100010001/02/09
Closing CommentsWhy Mini frac? Mini Frac can yield important information; k, P,presence of natural fractures, and leakoff information Results from Mini Frac can be used to fine tune thefrac design for vertical and Hz wells The closure pressure is used to estimate the criticaldraw-down during a well flowback to avoid poor fracperformanceThank You
Petro Management GroupQuality Petroleum Engineering ConsultantsHow to contact us ? E-mail: saad@petromgt.com Phone: (403) 216-5101 Cell:(403) 616-8330 Fax:(403) 216-5109 Address: #401, 100 - 4th Ave. S.W.Calgary, Alberta, Canada T2P 3N2
For a "fracture tip extension" leak-off, fracture closure is not observed. Therefore, a closure pressure can't be estimated An excessively long fall-off period is required to observe fracture closure Flowing back the well after the fall-off period, will induce fracture closure; and hence, allow an estimate of the closure pressure (P c).
A.2 ASTM fracture toughness values 76 A.3 HDPE fracture toughness results by razor cut depth 77 A.4 PC fracture toughness results by razor cut depth 78 A.5 Fracture toughness values, with 4-point bend fixture and toughness tool. . 79 A.6 Fracture toughness values by fracture surface, .020" RC 80 A.7 Fracture toughness values by fracture surface .
Fracture Liaison/ investigation, treatment and follow-up- prevents further fracture Glasgow FLS 2000-2010 Patients with fragility fracture assessed 50,000 Hip fracture rates -7.3% England hip fracture rates 17% Effective Secondary Prevention of Fragility Fractures: Clinical Standards for Fracture Liaison Services: National Osteoporosis .
injection) Code injection attacks: also known as "code poisoning attacks" examples: Cookie poisoning attacks HTML injection attacks File injection attacks Server pages injection attacks (e.g. ASP, PHP) Script injection (e.g. cross-site scripting) attacks Shell injection attacks SQL injection attacks XML poisoning attacks
This article shows how the fracture energy of concrete, as well as other fracture parameters such as the effective length of the fracture process zone, critical crack-tip opening displacement and the fracture toughness, can be approximately predicted from the standard . Asymptotic analysis further showed that the fracture model based on the .
hand, extra-articular fracture along metaphyseal region, fracture can be immobilized in plaster of Paris cast after closed reduction [6, 7]. Pin and plaster technique wherein, the K-wire provides additional stability after closed reduction of fracture while treating this fracture involving distal radius fracture.
6.4 Fracture of zinc 166 6.5 River lines on calcite 171 6.6 Interpretation of interference patterns on fracture surfaces 175 6.6.1 Interference at blisters and wedges 176 6.6.2 Interference at fracture surfaces of polymers that have crazed 178 6.6.3 Transient fracture surface features 180 6.7 Block fracture of gallium arsenide 180
Fracture is defined as the separation of a material into pieces due to an applied stress. Based on the ability of materials to undergo plastic deformation before the fracture, two types of fracture can be observed: ductile and brittle fracture.1,2 In ductile fracture, materials have extensive plastic
development teams. In Agile Product Management with Scrum, you’ll see how a product owner differs from a traditional product manager having a greater level of responsibility for the success of the product. The book clearly outlines and contrasts the different behav-iors between the traditional and the agile role.
