PETE 521 Engineering the Development of Unconventional Hydrocarbon Resources Lecture 8A: 1D Solutions Stress Interference: Between Perforation Clusters 1 Parts of this Lecture 1. US Shale Business News: Sale of Pioneer Natural Resources 2. Course Agenda Adjustments & Mid-Term Project Planning 3. 1D Stress Shadow Analysis Methodology 4. Strain Response Computations 2 Relax 3 Shale News • Oct 11, 2023: ExxonMobil acquires Pioneer via Merger; Pioneer suffered deeply during the oil price downturn. • Now sells for $59.5 billion; 856,000 acres; almost $70k/acre. • Jafurah 17,000 km2 ~ 4,200,792 acres; at $70k/acre Jafurah would be valued at $294 billion… • Pioneer currently has roughly 5,706 wells in production, Midland Basin. • Exxon says the acquisition represents 10 year drilling inventory replacement; 6,300 drilling locations (Enverus) • Previously, Dec 2009, ExxonMobil acquired XTO Energy in a $36 billion deal; 317,000 acres of the Marcellus. ? Scott Sheffield is one of the few Pioneer executives who will have a post-deal role – he is set to join Exxon’s board. 4 Oil Price DownTurn (2014-2020): Response and Performance Let’s briefly look at 4 companies: – Pioneer Natural Resources – South Western Energy – Range Resources – Laredo Energy Suffering during 2014-2020 downturn – First we look at Retained Earnings – Then at Headcount Reduction 5 WTI Crude Oil vs HH Natural Gas – 25 Year Daily Chart Tough Period US Shale Business 2014-2020 6 Pioneer Natural Resources Retained Earnings (Accumulated Deficit) 2006-2021 | PXD billions Excellent Financial mmt Acreage in Midland Basin Over its entire history, PXD generated ‘only’ $4 billion (+ dividends); is this company really worth $60 billion? 7 Pioneer Natural Resources: Number of Employees 2006-2021 | PXD 4,203 1,853 https://www.macrotrends.net/stocks/charts/PXD/pioneer-natural-resources/number-of-employees 8 Laredo Petroleum Retained Earnings (Accumulated Deficit) 2009-2021 | LPI Acreage in Midland Basin billions Disastrous Financial mmt Instead of Retained Earnings we see Accumulated Losses ($2.5 Billion) 9 Laredo Petroleum Number of Employees 2009-2021 | LPI 491 257 https://www.macrotrends.net/stocks/charts/LPI/laredo-petroleum/number-of-employees 10 Southwestern Energy Retained Earnings (Accumulated Deficit) 2006-2021 | SWN billions Acreage in Marcellus & Utica Shale Disastrous Financial mmt Instead of Retained Earnings we see Accumulated Losses ($7 Billion) 11 Southwestern Energy: Number of Employees 2006-2021 | SWN 2,781 900 12 Range Resources Retained Earnings (Accumulated Deficit) 2006-2021 | RRC billions Disastrous Financial mmt Instead of Retained Earnings we see Accumulated Losses ($4.5 Billion) 13 Range Resources Number of Employees 2006-2021 | RRC 990 533 https://www.macrotrends.net/stocks/charts/RRC/range-resources/number-of-employees 14 US E&P Bankruptcies (2015-2021) 15 Parts of this Lecture 1. US Shale Business News: Sale of Pioneer Natural Resources 2. Course Agenda Adjustments & Mid-Term Project Planning 3. 1D Stress Shadow Analysis Methodology 4. Strain Response Computations 16 2 Year Program MX-UHR Weijermars Mahmoud Ayranci Weijermars Ibrahim Abdulraheem Al Jawad 17 PETE 521 Course Plan 18 Mid-Term Project Compute a scalar measure for 1D stress intensity interference: • Start from Sneddon equations. Well Fracture Stage A • Simplify equations for our purpose. • First obtain some results in HW 8. Fracture Spacing B Perforation Cluster Toe • Then apply and complete analysis in Mid-Term Project, 3 fractures in the stage. 1D-analysis: along Lines A and B 19 Parts of this Lecture 1. US Shale Business News: Sale of Pioneer Natural Resources 2. Course Agenda Adjustments & Mid-Term Project Planning 3. 1D Stress Shadow Analysis Methodology 4. Strain Response Computations 20 Stress Shadowing Static Model • Complex process of stress and elastic strain interference initiated by spatial changes in the stress state around hydraulic fractures as they grow. • For adjacent fractures, if they are sufficiently close, we see interference of the stress changes induced by the opening of the fractures. Dynamic Model • Leads to curvature of the outer fractures and stumping off inner fractures. 21 Problem to be Solved Use Sneddon’s analytical solution. Let’s take a closer look at Sneddon equations (again) – good stuff never tires! Well Fracture Stage A A Fracture Spacing B Perforation Cluster B Toe C 1D-analysis: along lines A and B Simplified solutions we have previously used (HW3) for the 1D-solution along Line C. • Let’s look at that again, and see how it was obtained ( x2 =0 and θ= θ1= θ2=0). • Then we will do something similar for Lines A and B. 22 Sneddon Stress-Test Solution Simplified Solution   x3  xx = pNET 1 − 2 2 3/2   (x + L )   x3 + 2 xL2   yy = pNET 1 − 2 2 3/2   (x + L )   zz =  ( xx −  yy ) Fracture half-length = 100 ft Pnet =200 psi C 23 Sneddon Stress Function Solution 1. Radial coordinates to Cartesian: 2. The induced stress (delta): what is added to the existing stress due to opening of the crack (hydraulic fracture): Sneddon’s original solution is for Plane Strain boundary condition, meaning we have Δε33=0 ; so therefore Δσ33>0 3. Parameters affecting induced stress: • Fracture half-length (Wf or a) • Net pressure =pfrac-ppore-shmin (deviatoric) • Location (r, r1, r2, θ, θ1, θ2) distance to the fracture) • Poisson ratio v 24 Full Stress Tensor Solutions Pnet=200 psi; Wf=100 ft 25 Full Stress Tensor Solutions Pnet=200 psi; Wf=100 ft 26 Assignment HW8, Part A • Determine the simplified solution for the stress tensor elements along Line A • Plot the three solutions. • Also compute the associated strain tensor elements along Line A Pnet=2000 psi; Wf=100 ft 27 Parts of this Lecture 1. US Shale Business News: Sale of Pioneer Natural Resources 2. Course Agenda Adjustments & Mid-Term Project Planning 3. 1D Stress Shadow Analysis Methodology 4. Strain Response Computations 28 What is Strain? • Deformation of solids and fluids occurs due to a force causing displacement. • We can represent the force field by a stress tensor, and the displacement gradients by a strain tensor. • A constitutive equation links the stress and strain tensors Distortional displacements in elastic media and fluid bodies (dashed box region) can be described by compatibility equations (Weijermars and Ettehad, 2019). 29 For Non-Rigid Body Description of the elastic distortion process can take two possible paths: 1. Force -> Stress -> Strain 2. Displacement -> Strain-> Stress Whatever solution path you take, for elastic body deformation you’ll need to use the stress tensor Rigid Body Translation 1 2 http://www.conceptualdynamics.com/files/rbnewt/rbnewt_tran_page1.htm For rigid-body translation, no internal stresses need be computed to solve the displacement. There may be (elastic) stresses on the car body, but these are irrelevant for the rigid body dynamics. 30 Strain Tensor in Sneddon Context Sneddon’s original solution is for a Plane Strain boundary condition, meaning we have Δε33=0 ; so therefore Δσ33>0. So we only need to consider strains in the (x,y)-plane (because Δε33=0). What are these strains in the (x,y)-plane? Constitutive equation: σij=Cijkl = εij or For general 3D strain condition: 31 Strain Tensor for Plane Stress For general 3D Stress State For Plane Stress 32 Tensors for Plane Strain ε33=0 Sneddon gives you the stresses, and the associated strains follow from above constitutive equations 33 Written Out for Plane Strain Knowing the strain is interesting, because you can start to think how it may affect the aperture of a central fracture incase we have three perforation clusters per stage 34 Poisson Ratio = 0 No distinction between plane stress and plane strain possible when the Poisson ratio is zero; 35 Assignment HW8, Part A • Determine the simplified solution for the stress tensor elements along Line A • Plot the three solutions. • Also compute the associated strain tensor elements along Line A Pnet=2000 psi; Wf=100 ft 36 PETE 521 Engineering the Development of Unconventional Hydrocarbon Resources Lecture 8B: 1D Solutions Stress Interference: Between Fracture Tips 1 Cartoon of the Week 2 Parts of this Lecture 1. Line B solutions Frac Tip stresses 2. Stress Superposition 3. Proppant crushing 4. Proppant embedment 5. Mid-Term Project: What inputs are needed for a “realistic” or useful 1Dstress interference analysis? 3 Assignment HW8, Part B • Determine the simplified solution for the stress tensor elements along Line B • Plot the three solutions. • Also compute the associated strain tensor elements along Line B Pnet=2000 psi; Wf=100 ft Well Fracture Stage A Fracture Spacing B Perforation Cluster Toe 1D-analysis: along lines A and B Line B stresses trickier than Line A stresses, because: • Along line B the tensor elements are no longer principal stresses, there are shear stresses. • The principal stress orientations are systematically rotating as we move along line B. 4 Stress Trajectories • Stress trajectories show the principal stress orientations and how they rotate in space. • For the hydraulic fractures, see how the principal stress orientations change spatially. a) Prior to Fracturing b) During Fracturing A B Line B stresses is trickier than Line A stresses, because: • Along line B the tensor elements are no longer principal stresses, there are shear stresses. • The principal stress orientations are systematically rotating as we move along line B. 5 Stress Trajectories • Stress trajectories are tangent lines of the principal stresses (σ1 and σ2 ). Trajectories • Given by Isoclines • Tangent lines give stress trajectories • Contouring of same values give socalled stress trajectory isoclines 6 Line B solutions Use Sneddon’s analytical solution A B C 1D-solution along Line C really easy, because all angles in Sneddon become 0. 1D-solution along Line A also easy, because Ɵ=90, Ɵ1+Ɵ2 =180, r1=r2 and r=r1sinƟ1. 1D-solution along Line B: Ɵ2=90, r2=r sinƟ, more simplification? 7 Sneddon Stress Function Solution 1. Radial coordinates to Cartesian: 2. The induced stress (delta): what is added to the existing stress due to opening of the crack (hydraulic fracture): Sneddon’s original solution is for Plane Strain boundary condition, meaning we have Δε33=0 ; so therefore Δσ33>0 3. Parameters affecting induced stress: • Fracture half-length (Wf or a) • Net pressure =pfrac-ppore-shmin (deviatoric) • Location (r, r1, r2, θ, θ1, θ2) distance to the fracture) • Poisson ratio v 8 Strain and Stress Tensors for Plane Strain Knowing the strain is interesting, because you can start to think how it may affect the aperture of a central fracture incase we have three perforation clusters per stage 9 Parts of this Lecture 1. Line B solutions Frac Tip stresses 2. Stress Superposition 3. Proppant crushing 4. Proppant embedment 5. Mid-Term Project: What inputs are needed for a “realistic” or useful 1Dstress interference analysis? 10 Stress Superposition a) Prior to Fracturing • Stress superposition along Line A easy, because all stresses are principal stresses: σ11= σ1; σ22= σ2; σ33= σ3 • Nice thing about principal stresses is that you can simply sum them. • But as soon as there as the principal axes are angled with respect to the coordinate system, as applied to Line B, the tensor components need to be added using tensor addition rules, which involves the angles made by the principal stresses to the coordinate system axes. b) During Fracturing A B • Cumbersome to work with the stresses; one can switch to the strains and superpose them. Because the strains can be related to displacement vectors. 11 Shift Fracture and Superpose 12 Strain Doubling Up • Between two adjacent fractures, the displacements will double up but in a mirrored fashion. • If the distance is d, the total strain due to superposition is: • Total εyy(y)= εyy(y) + εyy(d-y) y d X • Same for principal stresses 13 Parts of this Lecture 1. Line B solutions Frac Tip stresses 2. Stress Superposition 3. Proppant crushing 4. Proppant embedment 5. Mid-Term Project: What inputs are needed for a “realistic” or useful 1Dstress interference analysis? 14 Proppant Strength •During hydraulic fracturing, we open the fractures by hydraulic fluid ‘transmitting’ the pressure •But after flowback, the elastic strain in the wall of the fracture wants to snap back and relax •The proppant must prevent fracture closure from happening •The relaxing elastic strain will exert point load pressures on the proppant grains; will the grains survive the pressure? 15 Micro-Proppant Tests TBA= Tetrabromobisphenol A and borosilicate mixture Mineral powder used was byproduct of pig iron smelting TBA 16 Mineral Powder Least Crush Mineral Powder gave highest Perm but at high closure stress loses its lead 17 Production Simulation Fracture Morphology Results suggest the micro-proppant boosts the well rate and cumulative 18 Data was from below paper 19 Parts of this Lecture 1. Line B solutions Frac Tip stresses 2. Stress Superposition 3. Proppant crushing 4. Proppant embedment 5. Mid-Term Project: What inputs are needed for a “realistic” or useful 1Dstress interference analysis? 20 Proppant Embedment Tremendous stresses where there are arches, pillars, low proppant concentrations, etc The complex geometries of hydraulic fracs are pushing companies towards using smaller, higher strength proppants to achieve greater transport and conductivity SPE 90698 21 Proppant Mechanisms during Flowback Katende et al., 2021 22 Impact on Production Katende et al., 2021 N Dakota (Besler et al., 2007) Weijermars (ARMA-IGS-2023-446) 23 Models for Mechanical Embedment Embedment Model Reviewed in Katende et al. (2021) 24 Parts of this Lecture 1. Line B solutions Frac Tip stresses 2. Stress Superposition 3. Proppant crushing 4. Proppant embedment 5. Mid-Term Project: What inputs are needed for a “realistic” or useful 1Dstress interference analysis? 25 Mid-Term Project Compute stress shadow magnitudes along lines A&B for a stage with three fractures. Show how the stress changes during the frac job fro a central fracture and for an outer fracture. What will be the final fracture aperture close to the perfs? Investigate in Sensitivity Analysis effect of reduced fracture spacing. How will the fracture aperture be affected? Assume proppant pads are emplaced near the perforations. What will be the proppent embedment after flow back? What crushing occurs? What will be the fracture aperture? 26 Inputs Needed? • Sneddon computes the change in stress in response to PNET • We can use the PFrac computed by Oshaish & Weijermars in ARMA paper, showing how it accumulates during the pump job. • Ppore is the reservoir pressure. • And σ3 = ISIP from frac report. PNET=Pfrac-Ppore-σ3 • Elastic properties follow from the geomechanical tests on core, or from the velocity logs in the well. • Values will all be given with HW8. 27 Stress Shadowing Static Model • Complex process of stress and elastic strain interference initiated by spatial changes in the stress state around hydraulic fractures as they grow. • For adjacent fractures, if they are sufficiently close, we see interference of the stress changes induced by the opening of the fractures. Dynamic Model • Leads to curvature of the outer fractures and stumping off inner fractures. 28
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