FEM-based modeling, simulation and calibration of ......Challenge of modeling hydraulic stimulation...

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FEM-based modeling, simulation and calibration of hydraulic fracturing for oil and gas applications

DYNARDO • © Dynardo GmbH 2014

Dr.-Ing. Johannes Will President Dynardo GmbH

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CAE-Consulting

Our expertise:

• Mechanical engineering

• Civil engineering & Geomechanics

• Automotive industry

• Consumer goods industry

• Power generation

Software Development

Dynardo is your engineering specialist for CAE-based sensitivity analysis, optimization, robustness evaluation and robust design optimization.

Founded: 2001 (Will, Bucher, CADFEM International)

More than 50 employees, offices at Weimar and Vienna

Leading technology companies Daimler, Bosch, Shell, Nokia, Siemens are supported by us


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Hydraulic fracturing

ANSYS UGM 2014 – Dynardo hydraulic fracturing simulator

In general the profitable production of unconventional shale gas requires stimulation of the reservoir rock.

Hydraulic fracturing is used to create a large and complex network of fractures which connects the production wells with the greatest possible volume of reservoir rocks:

• A horizontal wellbore is driven into the reservoir layer

• Water is pumped into the wellbore

• The water pressure is fracturing (enhancing natural fractures and creating new fractures) the jointed rock (shale).

• Sand (proppant) is added to keep fractures open after fluids have been removed and pressure has been subsided.


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Challenge of modeling hydraulic stimulation • Rock is initially jointed as well as new joints are created

• anisotropic deformation, strength and conductivity behavior dominate fracture growth

• Therefore 3D geometric model including deformation, strength and conductivity anisotropies is mandatory

• Rock mechanical challenge or the question: “Discrete or homogenized modeling of joints”

• Discrete joint modeling of stimulated volume in 3D result in computational and parameter overkill

• Therefore we used homogenized continuum approach which was established for 3D FEM simulation in jointed rock for dam applications in 1980’/90’s

• allows numerical efficiency for simulation as well calibration



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homogenized continuum approach mechanics

Major fault

Sets of joints: K1, K2, Sch

But major faults will be modelled “discrete” with a layer of volume elements, having plane of weakness and “matrix” material.

(picture from Wittke, W.: Rock Mechanics, Theory and Application with Case Histories, ISBN/EAN: 3540527192

Homogenized continuum approach does not model joints discrete. Jointed rock will be modelled as volume having “intact rock” and sets of strength anisotropies (joints). Matrix and joints will be evaluated at every discretization point!



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multiPlas – material law for jointed rock • Homogenized continuum approach: joints are modeled with

their discrete effects on strength, stress, conductivity at material point level

• multiPlas = multi-surface plasticity: combination of isotropic Mohr-Coulomb and Rankine yield surfaces for intact rock (material between joints) and anisotropic Mohr-Coulomb and tension cut-off yield surfaces for up to 4 joint sets

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isotropic Mohr-Coulomb yield surface for intact rock

anisotropic Mohr-Coulomb tension cut-off yield surfaces for joints

• The joint is represented by a plane x’-y’ (red)

• The joint orientation with respect to the global coordinate system (WCS) is defined by two orientation angles alpha (strike angle) and beta (dip magnitude)



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Simulation of fluid flow in jointed rock

• Hydraulic model is based on assumption of laminar flow at one or multiple (parallel) joints

• Flow is dominated by laminar flow in joints

• Homogenized fluid flow approach Darcy’s law

• Superposition of fluid flow in initial jointed rock mass rock and fluid flow in up to 4 joint sets results in anisotropic hydraulic conductivity matrix Dynardo provides an anisotropic hydraulic finite element for ANSYS (USER300)

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USERELEM USER300

t

hSR

s

q

• Flow equation (mass balance):

• Darcy’s law (momentum balance):

h Kq

t

hSR

z

hK

zy

hK

yx

hK

xszzyyxx

• Transient seepage equation (ground water

flow equation):

(Source: Wittke, W.: Felsmechanik; Springer-Verlag 1984)



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Parametric modeling of reservoir, well, fracture design

N

reference points

[XX6,YY6]

[XX5,YY5]

[XX3,YY3]

ST6

ST5

ST4

ST3

Stage 3 with 4 perforations

Well position



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Dynardo’s hydraulic fracturing simulator

• Tool for 3D simulations of hydraulic fracturing based on coupled hydraulic–mechanical finite element analysis

• Non-linear mechanical analysis using multi-surface plasticity material library multiPlas

• Anisotropic hydraulic element USER300

• APDL code for HM coupling, parametric modeling and post processing

Results/Outputs

Input parameters

FE-model

Initial pore pressure

Initial effective stress

Main loop

Mechanical analysis

Transient hydraulic analysis

fluid material properties update

stress state update

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USERELEM USER300



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Hydraulic fracturing needs calibration

• Because of the uncertain jointed rock and reservoir parameter the reservoir model needs advanced calibration procedure

• optiSLang is used for calibration of important model parameters with measurements (ISIP, slurry rate, bottom hole pressure, and seismic fracture measurements)

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USERELEM USER300

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Outputs

Input parameters

FE-model

Initial pore pressure

Initial effective stress

Main loop

Mechanical analysis

Transient hydraulic analysis

fluid material properties update

stress state update



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Because of the numerous uncertainties in reservoir conditions calibration of the simulator is mandatory and important. After calibration the reservoir model should have sufficient forecast quality to be used for optimization of hydraulic fracturing design. Dynardo‘s calibration process checks plausibility and balance of all inputs (single values and windows of uncertainties) including - ensure that in situ strength and stress/pore pressure values does

not result in plastic deformation - ensure that the model starts and stops fracturing at fracture

initialization/stop pressure - ensure that the model represents fracture growth in time and

space by match the pressure and the pumping rate histories - Ensure that the model represents the fracture direction,

extension, density as well as fracture barriers by matching micro seismic density functions

Calibration is the key



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Calibration is the key

MS1) Setting up a three dimensional model which can represent

reservoir conditions including in situ joint systems

- coupled fluid flow mechanical analysis, including propagation of fractures

MS2) Calibration of important model parameters with measurements (fracture initiation/stop pressure, bottom hole pressure and slurry rate signals and seismic fracture measurements)

MS3) Using the calibrated model for sensitivity analysis of operational conditions to understand the mechanism and to optimize the stimulation setup

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Collecting Jointed Rock Properties

Marble Falls Shale

Marble Falls Limestone

Barnett Shale A

Barnett Shale B

Barnett Shale C

Barnett Shale D

Ellenburger

Rock properties are extracted from core and log data as well as they are assumed from experience and literature.

More than 200 parameters: • Geometry, layering • Elastic properties of rock

and joints • Strength properties of

rock and joints • Permeability • In-situ stress and pore

pressure • Joint system orientation

3rd joint 170/80

joint for all rock units



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Calibration of reservoir model

Sensitivity evaluation of 200 rock parameter and the hydraulic fracture design Parameter due to seismic hydraulic fracture measurements

Blue:Stimulated rock volume Red: seismic frac measurement

With the knowledge about the most important parameter the update was significantly improved.

Hydraulic-mechanical coupling

Solver: ANSYS/multiPlas

Design evaluations: 160

Will J.: Optimizing of hydraulic fracturing procedure using numerical simulation; Proceedings

Weimarer Optimierung- und Stochastiktage 7.0, 2010, Weimar, Germany, www.dynardo.de


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Forecast of Gas Production • Forecast well is located 0,5 mile south of calibration well

• Forecast well used 6 active stages

• Stimulated volume of the two wells cross

Calibration well

Forecast well



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Forecast of Gas Production

real production FM_estimated dynardo Calibration well 24.48 MMscf 40 25 Forecast well 25.95 MMscf 71.5 27.5

• Seismic fracturing measurement estimated the total stimulated Barnett Shale volume to 266 e6 ft3 and the 6 month cumulative gas production is estimated to 71.5 MMscf.

• Using Dynardo simulator valuable stimulated rock volume was calculated to 103 e6 ft3 and 6 month cumulative Gas production of 27.5 MMscf.

103

27.5



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Pressured volume at 193 min (end of pressuring)

initial design stage1 Barnett Volume=24.2 e6

Improved frac design Barnett Volume=30.2 e6

By improving just one fracture design parameter, the stimulated volume could improve by 25%.

Optimization of Gas Production



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Application of Hydraulic Fracturing Analysis

other Reservoirs, US, Canada, China

2010 ongoing



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Simulator improvements since 2010/2011

following improvements are implemented: - Improvement of hydro mechanical coupling (Introduction of

influence of Joint Roughness Coefficient (JRC) and ratio of geometric and effective hydraulic opening to fluid flow in fractures

- calculation of “water accepting” and “proppant accepting” joint set

openings, volumes and related anisotropic conductivity updates - Introduction of perforation efficiency

calculate and calibrate jointed set opening, investigate stage interaction and sensitivities of reservoir parameter



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Visualization of geometric joint set openings normal to joint plane

3rd joint set 2nd joint set 1st joint bedding plane

joint set openings [in]

Simulator improvements



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Simulator improvements since 2012 - Improvement of parametric to model and calculate multiple stages at

multiple well to investigate well interaction - Investigation of “stress shadowing” between stages and wells - Implementation of stress dependent conductivity decline to run flow

back and production

- Implementation of mse density fit function



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Dynardo’s HFS Post Processor

© Dynardo GmbH 2013

During the calculation of hydraulic fracturing ANSYS post processing produce history plots to check and control

After solution there are multiple scripts available to produce standard post processing pictures

Post processing with standard ANSYS functionality is possible

In addition dynardo develope a high performance post processor for HFS.


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Impact to operation 2013 ongoing - Calculate connected proppant acceptant volume - Calculate drainage volume - Calculate accessible gas/oil initially in place

- Run sensitivity analysis to most important operational

parameters, create optimized meta models, use meta models for forecast of valuable volume and gas production

- Verify forecast quality of calibrated reservoir model with

production data - Include cost function to the optimization of hydraulic fracturing

setup



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Introducing best designs from sensitivity analysis and optimization using evolutionary based optimization we calculate the Pareto Frontier.

same EUR, lowest costs

best EUR without cost increase

optimal EUR highest costs

Impact to operation 2013 ongoing - Include cost function to the optimization of hydraulic fracturing design



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What is the optimal fracture design

Geomechanics

Rock & NF

Reservoir uncertainties &operational

parameter

Production Costs & EUR

Hydro-mechanical

coupling

Fluid flow analysis

Dynardo HFS + optiSLang identifies the main driver

and the reservoir potentials

How to solve the ccomplexity


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3. Calibrate the reservoir Model with best available data and proof forecast quality of reservoir model

1. Collect all available reservoir data

The Dynardo workflow

2. Built a parametric reservoir model of one or multiple wells

4. Scan space of possible completion scenario's and generate meta Models of Optimal Prognosis (MOP) how completion variation affects Estimated Ultimate Recovery (EUR) based on accessible gas/oil initially in place drainable from proppant accepting stimulated rock volume

6. Incorporate cost function for Unit Development Cost (UDC) and create the set of optimal completion designs to balance between increase of EUR and UDC

5. Based on MOP calculate EUR from neighboring wells, compare to real EUR production to result in a correlation function between Dynardo forecast and reality.


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Thank you for your attention!


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FEM-based modeling, simulation and calibration of ......Challenge of modeling hydraulic stimulation...

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