FEM-based modeling, simulation and calibration of hydraulic fracturing for oil and gas applications Dr.-Ing. Johannes Will President Dynardo GmbH

Transcription

1 FEM-based modeling, simulation and calibration of hydraulic fracturing for oil and gas applications Dr.-Ing. Johannes Will President Dynardo GmbH 1

2 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 Software Development Dynardo is your engineering specialist for CAE-based sensitivity analysis, optimization, robustness evaluation and robust design optimization. CAE-Consulting Our expertise: Mechanical engineering Civil engineering & Geomechanics Automotive industry Consumer goods industry Power generation 2

3 Hydraulic fracturing 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. 3

4 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 4

5 homogenized continuum approach mechanics 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! Major fault Sets of joints: K1, K2, Sch (picture from Wittke, W.: Rock Mechanics, Theory and Application with Case Histories, ISBN/EAN: But major faults will be modelled discrete with a layer of volume elements, having plane of weakness and matrix material. 5

6 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 + 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) 6

7 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 + USERELEM USER300 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) Flow equation (mass balance): q R S s h t Darcy s law (momentum balance): q K h Transient seepage equation (ground water flow equation): (Source: Wittke, W.: Felsmechanik; Springer-Verlag 1984) x K xx h x y K yy h y z K zz h z R S s h t 7

8 Parametric modeling of reservoir, well, fracture design N reference points [XX3,YY3] [XX5,YY5] ST4 ST3 Well position ST5 Stage 3 with 4 perforations [XX6,YY6] ST6 8 8

9 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 + + USERELEM USER300 Input parameters Main loop FE-model Initial pore pressure Initial effective stress fluid material properties update Transient hydraulic analysis Mechanical analysis stress state update Results/Outputs 9

10 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) + + USERELEM USER300 + Input parameters FE-model Main loop Transient hydraulic analysis Initial pore pressure fluid material properties update stress state update Outputs Initial effective stress Mechanical analysis 10

11 Calibration is the key 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 11 11

12 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 12 12

13 Collecting Jointed Rock Properties Rock properties are extracted from core and log data as well as they are assumed from experience and literature. Marble Falls Shale Marble Falls Limestone 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 Barnett Shale A Barnett Shale B Barnett Shale C 3 rd joint 170/80 joint for all rock units Barnett Shale D Ellenburger 13

14 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, 14

15 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 15

16 Forecast of Gas Production Seismic fracturing measurement estimated the total stimulated Barnett Shale volume to 266 e6 ft 3 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 ft 3 and 6 month cumulative Gas production of 27.5 MMscf real production FM_estimated dynardo Calibration well MMscf Forecast well MMscf

17 Optimization of Gas Production By improving just one fracture design parameter, the stimulated volume could improve by 25%. initial design stage1 Barnett Volume=24.2 e6 Improved frac design Barnett Volume=30.2 e6 Pressured volume at 193 min (end of pressuring) 17

18 Application of Hydraulic Fracturing Analysis other Reservoirs, US, Canada, China 2010 ongoing 18

19 Simulator improvements since 2010/2011 calculate and calibrate jointed set opening, investigate stage interaction and sensitivities of reservoir parameter 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 19

20 Simulator improvements Visualization of geometric joint set openings normal to joint plane 1 st joint bedding plane 2 nd joint set 3 rd joint set joint set openings [in] 20

21 Simulator improvements since 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 21

22 Dynardo GmbH 2013 Dynardo s HFS Post Processor 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. 22

23 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 23

24 Impact to operation 2013 ongoing - Include cost function to the optimization of hydraulic fracturing design Introducing best designs from sensitivity analysis and optimization using evolutionary based optimization we calculate the Pareto Frontier. optimal EUR highest costs best EUR without cost increase same EUR, lowest costs 24 24

25 What is the optimal fracture design Dynardo HFS + optislang identifies the main driver and the reservoir potentials Reservoir uncertainties &operational parameter Geomechanics Rock & NF How to solve the ccomplexity Production Costs & EUR Hydromechanical coupling Fluid flow analysis 25

26 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 3. Calibrate the reservoir Model with best available data and proof forecast quality of reservoir model 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. 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 2. Built a parametric reservoir model of one or multiple wells 1. Collect all available reservoir data The Dynardo workflow 26

27 Thank you for your attention! 27