4/16/2017 Hydraulic Fracturing Short Course, Texas A&M University College Station 2005 Fracture Design Fracture Dimensions Fracture Modeling Peter P. Valkó Fracture Design 2004

Source: Economides and Nolte: Reservoir Stimulation 3rd Ed.

Frac Design Goals

Well or Reservoir Stimulation? Near wellbore region and/or bulk reservoir? Acceleration versus increasing reserve? Low permeability Medium permeability High permeability Coupling of goals Frac&pack

Hydraulic Fracturing Design and Evaluation Why do we create a propped fracture? How do we achieve our goals? Data gathering Design Execution Evaluation

Fractured Well Performance Relation of morphology to performance Streamline view Flow regimes, Productivity Index, Pseudo-steady state Productivity Index, skin and equivalent wellbore radius

Well- Fracture Orientation MATCH Vertical well - Vertical fracture Horizontal well – longitudinal fracture MISMATCH (Choke effect) Horizontal well with a transverse vertical fracture Vertical well intersecting a horizontal fracture

Principle of least resistance Least Principal Stress Least Principal Stress Horizontal fracture Vertical fracture

Mismatch (Choked fracture) Typical mismatch situations: Horizontal well with a transverse vertical fracture Vertical well intersecting a horizontal fracture

Vertical Fracture - Vertical well Bypass damage Original skin disappears Change streamlines Radial flow disappears Wellbore radius is not a factor any more Increased PI can be utilized Dp or q

Longitudinal Vertical Fracture - Horizontal well sH,max xf sH,min Can it be done?

Transverse Vertical Fractures - Horizontal Well sH,max Hydraulic Fracture D xf sH,min Radial converging flow in frac

Fracture Morphology source: Economides at al.: Petroleum Well Construction

Main questions Which wellbore-fracture orientation is favorable? Which can be done? How large should the treatment be? What part of the proppant will reach the pay? Width and length (optimum dimensions)? How can it be realized?

Prod Eng 101 Transient vs Pseudo-steady state Productivity Index Skin

Pseudo-steady state Productivity Index 4/16/2017 Pseudo-steady state Productivity Index Production rate is proportional to drawdown, defined as average pressure in the reservoir minus wellbore flowing pressure Drawdown Circular: Dimensionless Productivity Index Fracture Design 2004

Hawkins formula Damage penetration distance

Exercise 1 Calculate the skin factor due to radial damage if 0.5 ft Damage penetration Permeability impairment 0.328 ft Wellbore radius Solution of Exercise 1 Note that any "consistent" system of units is OK.

Exercise 2 Assume pseudo-steady state and drainage radius re = 2980 ft in Exercise 1. What portion of the pressure drawdown is lost in the skin zone? What is the damage ratio? What is the flow efficiency? Solution 2 The fraction of pressure drawdown in the skin zone is given by (Since we deal only with ratios, we do not have to convert units.): Therefore 31 % of the pressure drawdown is not utilized because of the near wellbore damage. The damage ratio is DR = 31 % The flow efficiency is FE = 69 %.

Exercise 3 Assume that the well of Exercise 2 has been matrix acidized and the original permeability has been restored in the skin zone. What will be the folds of increase in the Productivity Index? (What will be the folds of increase in production rate assuming the pressure drawdown is the same before and after the treatment?) Solution 3 We can assume that the skin after the acidizing treatment becomes zero. Then the folds of increase is: The Productivity Index increase is 44 % , therefore the production increase is 44 % .

Exercise 4 Assume that the well of Exercise 2 has been fracture treated and a negative pseudo skin factor has been created: sf = -5. What will be the folds of increase in the Productivity Index with respect to the damaged well? Solution 4 The ratio of Productivity Indices after and before the treatment is The Productivity Index will increase 260 % .

Fully penetrating vertical fracture: Relating Performance to Dimensions wp 2xf h 2Vfp

Dimensionless fracture conductivity 2 xf w fracture conductivity no name Dimensionless fracture conductivity

Accounting for PI: sf and f and r’w sf is pseudo skin factor used after the treatment to describe the productivity JD is a function of what? half-length, dimensionless fracture conductivity Drainage radius, re sf is a function of what? half-length, dimensionless fracture conductivity wellbore radius, rw

Pseudo-skin, equivalent radius, f-factor Prats Cinco-Ley

Notation But JD is the best rw wellbore radius, m (or ft) r'w Prats’ equivalent wellbore radius due to fracture, m (or ft) Cinco-Ley-Samanieggo factor, dimensionless sf the pseudo skin factor due to fracture, dimensionless Prats' dimensionless (equivalent) wellbore radius But JD is the best

Example Assume rw = 0.3 ft and A= 40 acre 7 -4 36

Dimensionless Productivity Index, sf and f and r’w or Prats Cinco-Ley

Penetration Ratio Dimensionless Fracture Conductivity Proppant Number 4/16/2017 Penetration Ratio Dimensionless Fracture Conductivity Proppant Number 2 xf ye = xe xe Fracture Design 2004

The following models, graphs and correlations are valid for low to moderate Proppant Number, Nprop OK, so what IS the Proppant Number? The weighted ratio of propped fracture volume to reservoir volume. The weight is 2kf/k . A more rigorous definition will be given later. The following models are valid for Nprop <=0.1 ! (The case when the boundaries do not distort the streamline structure (with respect to lower proppant numbers.)

Prats' Dimensionless Wellbore Radius 0.01 0.1 1.0 10 100

Cinco-Ley and Samaniego graph f (CfD)= sf + ln(xf/rw) 1 2 3 4 0.1 10 100 1000 CfD f use f = ln(2) for CfD > 1000

Infinite or finite conductivity fracture Note that after CfD > 100 (or 30), nothing happens with f. Infinite conductivity fracture. Definition: finite conductivity fracture is a not infinite conductivity fracture (CfD < 100 or 30) (Other concept: uniform flux fracture, we will learn later.)

Various ways to look at it Proppant Number - Various ways to look at it Nprop= const means fixed proppant volume

Fig 1: JD vs CfD (moderate Nprop)

Fig 2: JD vs CfD (large Nprop)

OPTIMIZATION

Optimal length and width 2Vfp = 2h wp xf Struggle for propped volume: w and xf

The Key Parameter is the Proppant Number Medium perm High perm Frac&Pack

The Key Parameter is the Proppant Number Low perm Massive HF Medium perm

Let us read the optimum from the JD Figures Let us read the optimum from the JD Figures! dimensionless fracture conductivity (for smaller Nprop) penetration ratio (for larger Nprop)

Optimum for low and moderate Proppant Number CfDopt=1.6

Optimum for large Proppant Number

Tight Gas and Frac&Pack: the extremes Tight gas k << 1 md (hard rock) High permeability k >> 1 md (soft formation)

FracPi

Exercise No 1 Determine the "folds of increase" if 40,000 lbm proppant (pack porosity 0.35, specific gravity 2.6, permeability 60,000 md) is to be placed into a 65 ft thick formation of 0.5 md permeability. Assume all proppant goes to pay. The drainage radius is re = 2100 ft, the well radius is rw = 0.328 ft, the skin factor before fracturing is spre = 5. Determine the optimal fracture length and propped width.

1: Proppant Number 2: Max Folds of Increase 40,000 lbm proppant, specific gravity 2.6, pack porosity 0.35 packed volume is 40,000/62.4/2.6/(1-0.35) = 380 ft3 Folds of Increase FracPi 0.467 0.0768 FOI: 6.8 with respect to skin 5 FOI: 3.8 with respect to skin=0

Optimum frac dimensions The volume of two propped wing is 2V1wp = 380 ft3 If the proppant number is not too large: the optimal fracture half-length is The propped width is

Computer Exercise: High Perm Determine the optimal fracture length and propped width if 40,000 lbm proppant (pack porosity 0.35, specific gravity 2.6, permeability 60,000 md) is to be placed into a 65 ft thick formation of 50 md permeability. The drainage radius is re = 2100 ft, the well radius is rw = 0.328 ft, the skin factor before fracturing is spre = 5. (Assume all proppant goes to pay.)

Computer Exercise: Tight gas Determine the optimal fracture length and propped width if 40,000 lbm proppant (pack porosity 0.35, specific gravity 2.6, permeability 60,000 md) is to be placed into a 65 ft thick formation of 0.01 md permeability. The drainage radius is re = 2100 ft, the well radius is rw = 0.328 ft, the skin factor before fracturing is spre = 5. (Assume all proppant goes to pay.)

Economic optimization Production forecast Transient regime Stabilized Economics: Converting additional production into value Time value of money Discounted revenue NPV

Costs and Benefits The more proppant (larger proppant number) the higher Productivity Index, if the given proppant volume is placed according to the optimal dimensionless fracture conductivity The more proppant, the larger costs How large should be the treatment? NPV optimization

Treatment Sizing

Pre-Treatment Data Gathering

Design Input Data Petroleum Engineering Data Rock Properties Hydrocarbon in Place, Drainage area, Thickness, Permeability Rock Properties Young’s modulus, Poisson ratio, Fracture toughness, poroelastic const Stress State Leakoff Proppant and Other Fluid properties Operational constraints

Rock Properties Linear Elasticity Poroelasticity Fracture Mechanics 4/16/2017 Rock Properties Linear Elasticity Poroelasticity Fracture Mechanics Fracture Design 2004

Young's modulus and Poisson ratio Uniaxial test DD/2 l D l F A s xx F A = Linear stress-strain relations

Other elasticity constants

Formation Classification Two types Consolidated and tight E = 106 + psi Unconsolidated and soft E = 105 - psi

Poroelasticity and Biot’s constant Total Stress = Effective Stress + a[Pore Pressure]

Total Stress = Effective Stress + a[Pore Pressure] Who Carries the Load? Total Stress = Effective Stress + a[Pore Pressure] Grains Force Pore Fluid Biot’s constant a ~ 0.7

Stress State in Formations Far Field and Induced Stresses, Fracture Initiation and Orientation Stress versus Depth Minimum Horizontal Stress Magnitude and Direction

Total (absolute) horizontal stress The simplest model: 1) Poisson ratio changes from layer to layer 2) Pore pressure changes in time

Crossover of Minimum Stress 80x106 20x106 40x106 60x106 Stress, Pa Depth from original ground surface, m Original Vertical Stress True Vertical Stress Minimum Horizontal Stress Critical Depth 977 m -3000 -2500 -2000 -1500 -1000 -500 Current Depth , m Ground Surface

Stress Gradients Overburden gradient gradient Frac gradient Slope of the Vertical Stress line  1.1 psi/ft Frac gradient Basically the slope of the minimum horizontal stress line 0.4 - 0.9 psi/ft Extreme value: 1.1 psi/ft or more

Fracture width

Linear Elasticity + Fractures The force opening the fracture comes from net pressure Net pressure = fluid pressure - minimum principal stress pn = p - min The net pressure distribution determines the width profile Plane strain modulus and characteristic half length

Ideal Crack Shapes (Plane strain) Half length c pn(x) Deformation (distribution) net pressure (distribution) Plane - strain modulus: w Plane strain: Infinite repetition of the same picture (2D)

Shape of a pressurized crack, pn=cons Width pn : net pressure c : half length “characteristic dimension” Max Width w c linearity preserved

Height and Width in Layered Formation Questions: Far-field Stress Upper tip Contained? Breakthrough? Run-away? Up or Down? Width? Hydrostatic pressure? Height control? What can be measured? Pinch point Lower tip

From Fracture Mechanics to Fracture Height

Stress Intensity Factor weighted pressure at tip Pa · m1/2 psi - in.1/2 Weighting function: the nearer to tip, the more important the pressure value stress distribution at tip x c KI : proportionality const

Stability of Crack, Propagation Critical value of stress intensity factor: Fracture Toughness KIC Propagation: when stress intensity factor is larger than fracture toughness

Application: Fracture Height Prediction Height containment: why is it critical? Fracturing to water or gas Wasting proppant and fluid Can it be controlled? Passive: safety limit on injection pressure Active: proppant (light and heavy)

Calculation Based on Equilibrium Fracture Height Theory fluid pressure far field stress profile

Stress Intensity Factor at the Tips (calc) = Fracture Toughness of the Layer (given) Two equations, two unknowns

Penetration Into Upper and Lower Layers Klc,2 1 s2 Dhu yu s1 hp yd Dhd -1 s3 Klc,3

Notation

Input to a Height Map Calculation

Calculated Height Map (after HFM) Tip Location [ft] Tip Location [m] -1200 -1000 -800 -600 -400 -200 200 400 600 800 1000 3000 3100 3200 3300 3400 3500 3600 3700 3800 300 -300 21 26 psi MPa 100 -100 Tip Location [m] Tip Location [ft] Treating Pressure

How to Use a Height Map? 1 Off-line: Assume a height, make a 2D design, Calculate net pressure (averaged in time) Read-off a better estimate of height 2 In-line: P3D design (3D), Calculate net pressure at a location Adjust height to equilibrium

Fluid loss: the property of both the rock and the fluid 1 Leak-off 2 Spurt loss

AL Fluid Loss in Lab 2CL Sp y = 0.0024 + 0.000069x 10 20 30 40 50 60 10 20 30 40 50 60 Square root time, t1/2 (s1/2) 0.001 0.002 0.003 0.004 0.005 0.006 0.007 Lost volume per unit surface, m 2CL Sp AL

Fluid Loss in the Formation: Ct Flow through filtercake covered wall filtercake build-up and filtercake integrity Flow through polymer invaded zone “viscosity” of polymer in formation Flow in bulk of formation compressibility, permeability, viscosity of original reservoir fluid

Description of leakoff through flow in porous media and/or filtercake build-up 4/16/2017 Concept of leakoff coefficient Integrated leakoff volume: Leakoff Width Where are those “twos” coming from? What is the physical meaning? Fracture Design 2004

Step rate test Bottomhole pressure Injection rate Time

Step rate test Propagation pressure Two straight lines Injection rate Bottomhole pressure Propagation pressure Two straight lines

Fall-off (minifrac) Bottomhole pressure Injection rate Injection rate 3 ISIP 4 Closure 5 Reopening 6 Forced closure 7 Pseudo steady state 8 Rebound 1 5 2 3 4 8 6 Injection rate Bottomhole pressure Injection rate 2nD injection cycle 1st injection cycle 7 shut-in flow-back Time

Pressure fall-off analysis (Nolte)

g-function where F[a, b; c; z] is the Hypergeometric function, dimensionless shut-in time area-growth exponent where F[a, b; c; z] is the Hypergeometric function, available in the form of tables and computing algorithms

g-function

Pressure fall-off Fracture stiffness

Fracture Stiffness (reciprocal compliance) Pa/m

Shlyapobersky assumption No spurt-loss bN mN Ae from intercept pw g

Nolte-Shlyapobersky ( ) C m E t h - ' 4 p x 2 R 3 8 PKN a=4/5 KGD a=2/3 Radial a=8/9 Leakoff coefficient, C L ( ) N e f m E t h - ' 4 p x 2 R 3 8 Fracture Extent i b V ¢ = Width w 830 . 956 754 Fluid Efficiency Vi: injected into one wing