Modeling Proppant Transport in Fractures Using ANSYS. Dr. D. Dakshinamoorthy and Dr. Y. Dai ANSYS Inc

Transcription

1 Modeling Proppant Transport in Fractures Using ANSYS Dr. D. Dakshinamoorthy and Dr. Y. Dai ANSYS Inc 1

2 Outline: Proppant Transport Using ANSYS Overview of proppant transport in fractures Factors affecting proppant transport Numerical modeling challenges ANSYS solutions Present the results for proppant transport simulations Conclusions and Future work 2

3 Proppant Transport: Overview Hydraulic fracturing Increase the productivity of oil & gas well (1) Frac fluid slurry Mixture of frac fluid and proppant is injected into the high pressure (2) Fluid pressure Generates fractures extending into the rock medium (2) Width of the fracture is maintained by the transported proppant (2) 3 Reference: 1. Patankar, N.A., Joseph, D.D., Wang, J., Barree, R.D., Conway, M., Asadi, M., Power law correlations for sediment transport in pressure driven channel flows. International Journal of Multiphase Flow Ouyang, S., Carey, G. F., Yew, C. H., An adaptive element scheme for hydraulic fracturing with proppant transport. International Journal of Numerical Methods in Fluids

4 Concerns in Proppant Transport Where is Proppant Going? Better proppant placement What should be the injection rate? Proppant selection Longer propped fractures Lateral Spreading Use of high viscous frac fluids Height growth Vertical filling 4

5 Proppant Transport: Overview Complex multiphase flow problem Proppant settles to the bottom Mound develops Reaches an equilibrium height Until the equilibrium height Proppant bed gets higher and then it spreads laterally Reference: Patankar, N.A., Joseph, D.D., Wang, J., Barree, R.D., Conway, M., Asadi, M., Power law correlations for sediment transport in pressure driven channel flows. International Journal of Multiphase Flow

6 Proppant Transport: Stages Various Stages in Proppant Transport (2) Stage 1: Convection / settling dominated. Stage 2: Buildup of a proppant bed. Stage 3: Steady state saltation over bed. Stage 4: Final settling after flow shutoff. Stage 1, 2 & 4 Settling Process Stage 3 Wash Out process (1) 6 Reference: 1. Patankar, N.A., Joseph, D.D., Wang, J., Barree, R.D., Conway, M., Asadi, M., Power law correlations for sediment transport in pressure driven channel flows. International Journal of Multiphase Flow Sharma, M.M., Copeland, D., Gadde, B. P., Liu, Y., Norman, J., Bonnecaze, R., Advanced Fracturing Technology for Tight Gas: Where is the Proppant Going? COGA Conference.

7 Proppant Transport: Settling Process Settling process is governed by settling laws Terminal settling velocities Quantifies the process Empirical Equations are usually used: Single particle Stokes Law for laminar flow Allen s Equation for transition flow Newton s Equation for turbulent flow Single particle settling laws are not enough to determine the settling process of the proppant in fractures 7

8 Proppant Transport: Settling Process Hindered settling Particle to Particle interaction Wall effects (or retardation) Leak off Frac fluid can leak Reference 1. Sharma, M.M., Copeland, D., Gadde, B. P., Liu, Y., Norman, J., Bonnecaze, R., Advanced Fracturing Technology for Tight Gas: Where is the Proppant Going? COGA Conference. 8

9 Proppant Transport: Washout Process Sliding or Slipping Bed load transport Advection after fluidization by lift Suspended loaded transport Efficient Lift force plays an important role in re suspension of particles Complex physics and requires detailed modeling Reference: Patankar, N.A., Joseph, D.D., Wang, J., Barree, R.D., Conway, M., Asadi, M., Power law correlations for sediment transport in pressure driven channel flows. International Journal of Multiphase Flow

10 ANSYS: Models for Particulate Flows Model Numerical approach Particle fluid interaction DPM Fluid Eulerian Particles Lagrangian Empirical models for sub grid particles Particle Particle interaction Particles are treated as points Particle size distribution Easy to include PSD because of Lagrangian description DDPM KTGF Fluid Eulerian Particles Lagrangian Empirical; sub grid particles Approximate P P interactions determined by granular models Easy to include PSD because of Lagrangian description DDPM DEM Fluid Eulerian Particles Lagrangian Empirical; sub grid particles Accurate determination of P P interactions. Can account for all PSD physics accurately including geometric effects Euler Granular model Fluid Eulerian Particles Eulerian Empirical; sub grid particles P P interactions modeled by fluid properties, such as granular pressure, viscosity, drag etc. Different phases to account for a PSD; when size change operations happen use population balance models Macroscopic Particle Model Fluid Eulerian Particles Lagrangian Interactions determined as part of solution; particles span many fluid cells Accurate determination of P P interactions. Easy to include PSD; if particles become smaller than the mesh, uses an empiricial model 10

11 DEM Analysis The proppant transport process can be analyzed using Lagrangian tracking process ANSYS FLUENT does offer DEM (Discrete Element Modeling) for analyzing large number of particles Collision and frictional terms are modeled discretely Understand the extent and limitations of this approach 11

12 DEM DEM modeling of Proppant Transport 12

13 Macro Particle Model ANSYS FLUENT does offer Macro Particle Model (MPM) as a solution for suspended bed transport? Lift and Drag are explicitly calculated or predicted by the MPM model No empirical correlations are needed 13

14 MPM Lift Force Example Demonstrate Particle Lift Off from ground using MPM Geometry of a long narrow channel (200 X 75 microns) Steady state periodic flow field was solved in the channel A 20 microns diameter particle was placed on bottom surface of the channel Transient MPM simulation was performed for particle trajectory. Fine mesh (about 4 fluid cells across particle diameter) Initial Location of the Particle 14 Flow Direction

15 MPM Validation Lift Force DistancefromWal (microns) Axial Distance (microns) Axial Distance (in microns) Particle Trajectory Distance from Wall (in microns) MPM automatically predicts particle lift force without including any lift force correlation (Saffman etc) 15

16 Proppant Transport: Euler Granular Current Study: Euler Granular model is considered for studying settling in fractures Every phase has its own mass, momentum and energy conservation Conservation equations of different phases are coupled via interfacial terms these terms are modeled. Granular model does have intrafacial terms to account for collision and friction Closeness of these terms to reality determines accuracy of the model 16

17 Proppant Transport: Granular Model Granular flows are dense so drag coefficients are based on single particle drag + concentration effect Hindered settling is considered Collisional and frictional effects (becomes important near packing limit) are considered Wall effects are also considered 17

18 Proppant Transport: Solution Domain Fracture Width = 0.5 cm 40 ft 300 ft Typical Fracture is Considered 18

19 Parameters for Proppant Transport Study Fracture Geometry Fluid Properties Proppant Size and Properties Injection Rates Proppant Concentration in Frac Fluid and Leakoff Rates Modeled using UDF 19

20 Proppant Transport: Boundary Conditions Full 3D Wall Effects and Leak Off Modeled Slurry flow: Mixture of Frac Fluid and Proppant Fracture Width = 0.5 cm 40 ft 300 ft v 0 V 0.75V V Leak 0 0 v L v0 Leak Off Rates v L 20

21 Proppant Transport: Conditions Fluid density: Kg/m 3 Particle density: 2500 Kg/m 3 Fluid viscosity: 1 cp Diameter of particle: 100 µm, 300 µm & 500 µm Particle concentration: 20% Fluid horizontal velocity: 0.4 m/s Terminal Settling Velocity = 0.9 cm/s, 7.5 cm/s & 20.5 cm/s 21

22 Typical Results: Contours of Velocity Frac Fluid Velocity Velocity Decreases Due to Leak off Settled Bed after t secs 22

23 Typical Results: Contours of Velocity As state earlier early injected proppant settles and forms a mound and reaches an equilibrium height. The velocity in the gap increases as the mound grows, which allows the later injected proppant to settle and spread laterally. Proppant Velocity Settled Bed after t secs 23

24 Typical Results: Contours of Pressure Pressure drop across the fracture can be calculated during the settling process Settled Bed after t secs 24

25 Typical Results: Contours of Volume Fraction of Proppant Bed Height Extent of proppant placement Settled Proppant Bed after t secs Proppant Volume Fraction 25

26 This image cannot currently be displayed. This image cannot currently be displayed. 300 µm Vs 500 µm Settling 300 µm Proppant 500 µm Proppant Settling of Two Different Proppant Sizes 26

27 Snapshots of 300 µm and 500 µm 300 µm 500 µm time 27

28 Proppant Transport: Wash Out Process Can Euler Granular model capture washout process? Sliding or Slipping Bed load transport can be captured by Euler Granular Model A small fraction of the bed is patched with proppant and the bed load transport is studied Two proppant sizes are investigated 28

29 This image cannot currently be displayed. This image cannot currently be displayed. Proppant Transport: Wash Out Process 300 µm Proppant 100 µm Proppant 29

30 This image cannot currently be displayed. Proppant Transport: Wash Out Process 30

31 Proppant Transport: Wash Out Process Euler Granular model is capturing the effect of wash out process 300 µm Proppant mound didn t wash out The mound created a re circulating zone upstream and allowed settling in this zone The mound also grew over a period of time 100 µm Proppant mound did wash out. The mound started loosing proppant and the height decreased This is not due to saltation or suspended bed transport only due to bed load transport 31

32 Results Discussion The results clearly shows the value of using Euler Granular model to capture the settling and wash out process Euler Granular model does capture the effect of hindered settling, leak off and retardation on the proppant transport in fractures Euler Granular model can clearly be used for studying the bed load transport process 32

33 Thank you Very Much Questions or Comments!!!!! 33