Modeling, Monitoring, Post-Job Evaluation, Improvements Hydraulic Fracturing Short Course, Texas A&M University College Station 2005 Modeling, Monitoring, Post-Job Evaluation, Improvements Tamu Frac Modelling 2004

3D

P3D and 3D Models FracPro (RES, Pinnacle Technologies) FracCADE (Dowell) Stimwin (Halliburton) and PredK (Stim-Lab) TerraFrac StimPlan MFrac

Dimensionless Form of Nordgren Model tD(xfD) : inverse of xfD(tD) xD = 0 (wellbore) xD = xfD (tip)

Propagation Criterion of the Nordgren Model Net pressure zero at tip Once the fluid reaches the location, it opens up immediately Propagation rate is determined by “how fast the fluid can flow

Other Propagation Criteria (Apparent) Fracture Toughness Dilatancy Statistical Fracture mechanics Continuum Damage mechanics

Fracture Toughness Criterion Stress Intensity Factor KI =pnxf1/2 KI xf hf pn KIC (Rf)

CDM What is the time needed for D to start at D = 0 and grow to D = 1 ?

CDM Propagation Criterion Combined Kachanov parameter:

P3D Pseudo 3 D Models: Extension of Nordgren’s differential model with height growth Height criterion Equilibrium height theory or Assymptotic approach to equilibrium Plus some “tip” effect

3D (Finite Element Modeling) x y wellbore element tip element

Fracture Toughness Criterion Fluid flow in 2 D Fluid loss according to local opening time Propagation: Jumps Stress Intensity Factor KI > KIC ? pn KIC

Data Need for both P3D and 3D: Layer data Permeability, porosity, pressure Young’s modulus, Poisson ratio, Fracture toughness Minimum stress Fluid data Proppant data Leakoff calculated from fluid and layer data

Design Tuning Steps Step Rate test Minifrac (Datafrac, Calibration Test) Run design with obtained min (if needed) and leakoff coefficient Adjust pad Adjust proppant schedule

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 g=0

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

1: g-function plot of pressure 2: get parameters bN and mN 3 Calculate Rf (fracture extent -radius) 4 Calculate CLAPP (apparent leakoff coeff) 5 Calculate wL (leakoff width) 6 Calculate we (end-of pumping width) 7 Calculate h (fluid efficiency)

Computer Exercise 3-1 Minifrac analysis

Example Permeable (leakoff) thickness, ft, 42 Plane strain modulus, E' (psi), 2.0E+6 Closure Pressure, psi, 5850 Time, min BH Injection rate, bpm BH Pressure, psi Include into inj volume Include into g-func fit 0.0 9.9 1 1.0 21.8 9.9 0.0 1 21.95 7550.62 22.15 7330.59

Output Slope, psi -4417 Intercept, psi 13151 Injected volume, gallon 9044 Frac radius, ft 39.60 Average width, inch 0.49205 Fluid efficiency 0.16708 Apparent leakoff coefficient (for total area), ft/min^0.5 0.01592 Leakoff coefficient in permeable layer, ft/min^0.5 0.02479

From "apparent" to "real“ (radial)

Redesign Run the design with new leakoff coefficient (That is why we do minifrac analysis)

Monitoring Calculate proppant concentration at bottom (shift) Calculate bottomhole injection pressure, net pressure Calculate proppant in formation, proppant in well Later: Add and synchronize gauge pressure

Normal frac propagation Nolte-Smith plot Wellbore screenout Log net pressure Tip screenout Normal frac propagation Unconfined height growth Log injection time

Post-Job Logging Tracer Log Temperature Log Production Log

Available Techniques for Width and Height Measured Directly Formation Micro Scanner Borehole Televiewer Based on Inference Temperature Logging Isotopes (fluid, proppant) Seismic Methods, Noise Logging Tiltmeter techniques Spinner survey Radius of penetration

Sc Sb Ir Tracer log

Tiltmeter Results after Economides at al. Petroleum Well Construction

Pressure Match with 3D Simulation

3D Simulation FracCADE Flow Capacity Profiles 50 100 150 200 250 Texaco E&P OCS-G 10752 #D-12 Actual Flow Capacity Profiles 05-23-1997 50 100 150 200 250 Fracture Half-Length - ft 0.05 0.10 0.15 0.20 0.25 Propped Width - in 1000 2000 3000 4000 5000 Conductivity (Kfw) - md.ft Propped Width (ACL) Conductivity - Kfw *Mark of Schlumberger

Well Testing: The quest for flow regimes

Design Improvement in a Field Program Sizing Pad volume for “generic” design More aggressive or defensive proppant schedule Proppant change (resin coated, high strength etc.) Fluid system modification (crosslinked, foam) Proppant carrying capacity Leakoff Perforation strategy changes Forced closure, Resin coating, Fiber reinforcement, Deformable particle

Example: Tortuous Flow Path Analysis of the injection rate dependent element of the treating pressure Does proppant slug help? Does limited entry help? Does oriented perforation help? Extreme: reconsidering well orientation: e.g. S shaped

Misalignment

Fracture Orientation: Perforation Strategy after Dees J M, SPE 30342 smax From overbalanced perforation From underbalanced perforation Tamu Frac Modelling 2004

High Viscosity slugs

Proppant Slugs

Case Study: Effect of Non-Darcy Flow Forcheimer Equation Cornell & Katz

Non-Darcy Flow Dimensionless Proppant Number is the most important parameter in UFD Effective Proppant Pack Permeability

Non-Darcy Flow Effective Permeability Reynolds Number keff is determined through an iterative process Drawdown is needed to calculate velocity Reynolds Number

Non-Darcy Flow Coefficient (b) Several equations have been developed mostly from lab measurements (empirical equations) General form of b equation where b is 1/m and k is md

SPE 90195 Optimum FractureTreatment Design Minimizes the Impact of Non-Darcy Flow Effects Henry D. Lopez-Hernandez, SPE, Texas A&M University, Peter. P. Valko, SPE, Texas A&M University, Thai T. Pham, SPE, El Paso Production

Case Study: Reynolds number

Case Study: Proppant number

Case Study: Max possible JD

Case Study: Optimum frac length

Case Study: Optimum frac width

Summary Increasing role of evaluation Integration of reservoir engineering, production engineering and treatment information Cost matters Expensive 3D model does not substitute thinking Still what we want to do is increasing JD Tamu Frac Modelling 2004