1. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 1/18 A Numerical Study of Nonideal and Secondary Fractures in Shale-gas Reservoirs using Voronoi Grids Thesis Defense 27 May 2011 — College Station, Texas Olufemi OLORODE Department of Petroleum Engineering Texas A&M University College Station, TX 77843-3116 (USA) +1.803.397.7623 — olufemi.olorode@pe.tamu.edu

2. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 2/18 Objectives: ● To present an unstructured mesh-maker that is used in gridding complex and non-ideal fracture geometries ● To study the effects of nonplanar and nonorthogonal fractures on reservoir performance ● To study the interaction between secondary and primary fractures ● To assess the validity of single-fracture representation of multiply-fractured horizontal wells

3. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 3/18 Motivation: ● Cartesian grids do not provide the flexibility of modeling irregular fracture geometries. ● Cartesian grids require far more grid-blocks, many of which are unnecessary. ● No consensus on the effect of nonideal fracture geometries on production. ● Very little is known about the interaction between induced and hydraulic fractures (Houze et al. 2010). Voronoi grids showing nonplanar fractures Cartesian Mesh showing 4 planar fractures Unnecessary refinement X Y X Y

4. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 4/18 Approach: 324m 260 x Magnification ~100μm Relative Sandstone Pore Diameter Relative Shale Pore Diameter Visualize the grids Develop Meshmaker Construct Voronoi grids Analyze rates using log-log plots Perform simulation Provide pressure maps where needed Any bugs? Base case? Debug code Yes No Validate with Ecrin

5. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode x mf = n*x f Slide — 5/18 Gridding: Single-fracture Representation 3D View SRV Unstimulated Reservoir Volume X-axis Y-axis 12345 xfxf n=6 2D View Horizontal well Fractures Y Z X Y X

6. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 6/18 Results: Log-log Rate Profile ● Discussion: Single-fracture Representation of Multiple Fractures ■ Fracture interference is absent in single fracture case ■ Boundary-dominated flow is not seen in the single fracture case Single fracture Representation 10 multi-stage fractures 1 month 5 years 1 year 30 years

7. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 7/18 Results: Distinguishing between k f and w f ● Conductivity is kept constant at 492 md-ft (1.5x10 -10 mm- m 2 ). ● Do we see distinct trends at early times? w f, ftk frac, md  modified 0.01050,000 0.33 0.04910,000 0.066 0.098 5,000 0.033 0.328 1,5000.0099 Table 1—Fracture parameters in field units

8. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 8/18 Results: (after porosity modification) ● Porosity modification keeps mass accumulation constant ● Bad news:  we cannot distinguish between k f and w f. ● Good news:  we can represent very minute fracture cells with much bigger cells. where, Porosity Modification:

9. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 9/18 Background: Nonplanar & Nonorthogonal Fractures Nonorthogonal fracture l t = a l a = a sin θ where, l t is total length, and l a is apparent length f e d b c θ a h = a sin θ Nonplanar fracture l t = b+c+d+e+f l a = l t sin θ where, l t is total length, l a is apparent length, All segments are inclined at angle θ to the horizontal. 3D Schematic of a Nonplanar Fracture 2D Schematic of a Nonplanar Fracture 3D and 2D Schematics of a Nonorthogonal Fracture Illustration of “Total” and “Apparent” Lengths

10. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 10/18 Gridding 2D Aerial View of Nonplanar Fractures 2D Aerial View of Nonorthogonal Fractures Y X Y X

11. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 11/18 Results: Nonorthogonal and Nonplanar Fractures ● Discussion: ■ Irregularities in the fracture geometry limits flow-regime analysis with diagnostic rate plots

12. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 12/18 Results: Nonorthogonal and Nonplanar fractures ● Discussion: ■ The cumulative production initially matches that of a planar fracture with x f =l t, but drops gradually over time. xf=ltxf=lt xf=laxf=la Nonplanar frac Nonorthogonal frac

13. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 13/18 Gridding: Secondary Fractures ■ Three secondary fracture configurations are studied: — A secondary fracture that intersects the primary fracture at height, h/4. — A centered secondary fracture. — Two secondary fractures at heights h/4 and 3h/4, respectively. Y X Z h/4 h/2 h/4

14. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 14/18 Results: Secondary Fracture Flow Profile ● Parallel half-slope lines depict linear flow into the SRV. ● Increase in rates correspond to the increase in the SRV that is drained into the wells. ● Change in slope at late times indicate outset of boundary- dominated flow. ● NB: Secondary fractures were modeled with infinite conductivity, and are 0.05 mm (0.00016 ft) wide. 2 secondary fracs Centered secondary frac Secondary frac at h/4 Primary fracs only

15. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 15/18 Results: Effect of Secondary Fracture Conductivity ● Discussion: ■ Dimensionless rate profiles show a reduction in the linear half-slope when the dimensionless conductivity of the secondary fractures becomes less than 10 (finite conductivity) ■ This may be useful in optimizing fracture design k frac, mdC f, md-ftC fD 3x10 6 4.92x10 2 1.67x10 4 2x10 6 3.28x10 2 1.11x10 4 1x10 6 1.64x10 2 5.56x10 3 2x10 5 3.28x10 1 1.11x10 3 1x10 5 * 1.64x10 1 5.56x10 2 1x10 4 1.64x10 0 5.56x10 1 2x10 3 3.28x10 -1 1.11x10 1 1x10 3 1.64x10 -1 5.56x10 0 2x10 2 3.28x10 -2 1.11x10 0 Table 2—Secondary fracture conductivity parameters

16. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 16/18 Results: Effect of Primary Fracture Conductivity ● Discussion: ■ Dimensionless rate profiles show a drop in production as the primary fracture conductivity drops ■ Results match those published by Freeman et al. (2010) k frac, mdC f, md-ftC fD 5.00x10 6 4.92x10 4 1.67x10 6 5.00x10 5 4.92x10 3 1.67x10 5 5.00x10 4 4.92x10 2 1.67x10 4 5.00x10 3 4.92x10 1 1.67x10 3 5.00x10 2 4.92x10 0 1.67x10 2 1.64x10 0 5.56x10 1 3.33x10 1 3.28x10 -1 1.11x10 1 1.67x10 1 1.64x10 -1 5.56x10 0 3.33x10 0 3.28x10 -2 1.11x10 0 Table 3—Primary fracture conductivity parameters

17. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 17/18 Conclusions: ● Irregularities in fracture geometry can limit the analysis of these reservoirs with diagnostic plots. ● Production increases as SRV increases for infinite- conductivity secondary fractures. ● All infinite-conductivity secondary fractures with the same SRV have identical flow behavior, while finite-conductivity secondary fractures show a reduction in magnitude of the half-slope line.

18. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 18/18 A Numerical Study of Nonideal and Secondary Fractures in Shale-gas Reservoirs using Voronoi Grids End of Presentation Thesis Defense 27 May 2011 — College Station, Texas Olufemi OLORODE Department of Petroleum Engineering Texas A&M University College Station, TX 77843-3116 (USA) +1.803.397.7623 — olufemi.olorode@pe.tamu.edu

19. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Questions? Slide — 19/18

20. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 20/18 Parameters SI UnitField Unit Frac half-length, x f 90 m 300 ft Frac width, w f 3 mm 0.00984 ft Frac spacing, d f 100 m 328 ft Well length, L w 1200 m 4000 ft Number of fracs 12 Reservoir thickness, h 100 m 330 ft Permeability, k shale 1.0x10 -19 m 2 1.0 x10 -4 ft Frac permeability, k frac 5.0x10 -11 m 2 5.0 x10 4 ft Porosity,  4 % Frac porosity,  frac 33 % Temperature, T 93.33 0 C 200 0 F Well radius, r w 0.1 m 0.32 ft Reservoir pressure, p i 3.45x10 7 Pa 5000 psia Well pressure, p wf 3.45x10 6 Pa 500 psia Table 1.1—Representative Barnett Shale-gas Parameters

21. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 21/18

22. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 22/18

23. 27 May, 2011 — College Station, TX Study of Nonideal and Secondary Fractures O.M. Olorode Slide — 23/18