1. Produced Water Reinjection Performance Joint Industry Project TerraTek, Inc. Triangle Engineering Advantek International TAURUS Reservoir Solutions Ltd. Phalanx Software Solutions TerraTek, Inc. Triangle Engineering Advantek International TAURUS Reservoir Solutions Ltd. Phalanx Software Solutions

2. Horizontal Wells: Injectivity Analysis - Survey of Tools and Methods Tony Settari TAURUS Reservoir Solutions Ltd. Injectivity Analysis - Survey of Tools and Methods Tony Settari TAURUS Reservoir Solutions Ltd.

3. Why Do We Need to Predict PWRI Injectivity by Classical Methods?  Establish baseline for unfractured well  Detect abnormal decrease or increase in injectivity due to solids plugging, geomechanical effects, etc.  Provide estimates for expected injectivity increase due to fracturing  Establish baseline for unfractured well  Detect abnormal decrease or increase in injectivity due to solids plugging, geomechanical effects, etc.  Provide estimates for expected injectivity increase due to fracturing

4. 1. Unfractured Horizontal Well (Clean Water)  Number of analytical approximations available: Babu & Odeh Goode & Kuchuk Joshi  Numerically based work Gilman & Jargon  Accuracy of analytical methods varies and can be poor!  Number of analytical approximations available: Babu & Odeh Goode & Kuchuk Joshi  Numerically based work Gilman & Jargon  Accuracy of analytical methods varies and can be poor!

5. Comparison of Analytical Methods Unfractured Well (Kuppe & Settari, 1998)  Problem solved: Horizontal well of length=400 ft in a square reservoir, const. press. or no flow outside boundary, single phase flow  Predict steady state (or pseudo-steady state) PI or II  Use existing analytical methods and numerically derived answers  Problem solved: Horizontal well of length=400 ft in a square reservoir, const. press. or no flow outside boundary, single phase flow  Predict steady state (or pseudo-steady state) PI or II  Use existing analytical methods and numerically derived answers

6. Comparison of Analytical Methods Unfractured Well (Kuppe & Settari, 1998)  Injectivity index calculated by 3 analytical methods and simulation  Single phase flow  Injectivity index calculated by 3 analytical methods and simulation  Single phase flow

7. Comparison of Analytical Methods Unfractured Well (Kuppe & Settari, 1998)

8. Numerical Modeling of Unfractured Horizontal Wells (Clean Water)  Routine now, but often done poorly Requires fine gridding for accuracy (or numerically derived well index values within large grids) - results in big models Problems in representing k v /k h anisotropy if grid is not aligned with k tensor High angle or meandering wells: conflicting requirements for gridding along the wellbore or along the layers Wellbore friction pressure drop modeling Representation of “smart wells”, etc.  Routine now, but often done poorly Requires fine gridding for accuracy (or numerically derived well index values within large grids) - results in big models Problems in representing k v /k h anisotropy if grid is not aligned with k tensor High angle or meandering wells: conflicting requirements for gridding along the wellbore or along the layers Wellbore friction pressure drop modeling Representation of “smart wells”, etc.

9. 1. Unfractured Horizontal Well (with permeability damage)  No analytical methods for horizontal wells? Possible adaptation of WID model?  Numerically possible but definition of plugging must be provided requires special coding  No “off the shelf” tools currently?  Tools for layered formation (other than simulators)?  No analytical methods for horizontal wells? Possible adaptation of WID model?  Numerically possible but definition of plugging must be provided requires special coding  No “off the shelf” tools currently?  Tools for layered formation (other than simulators)?

10. Fractured Horizontal Wells  There are two types and two orientations of fractures Static Fractures (constant surface area and conductivity with injection/production - conductivity and width can vary if it is coupled with a geomechanical model) Dynamic Fractures (changing geometry and conductivity with injection/production) Longitudinal Fracture (along well) Transverse Fracture (perpendicular to well)  There are two types and two orientations of fractures Static Fractures (constant surface area and conductivity with injection/production - conductivity and width can vary if it is coupled with a geomechanical model) Dynamic Fractures (changing geometry and conductivity with injection/production) Longitudinal Fracture (along well) Transverse Fracture (perpendicular to well)

11. Static Fractures

12. 2. Fractured Horizontal Wells - Clean Water: Static fracs (Propped, Acidized)  Karcher et al. Numerically derived for single transverse fracture  Mukherjee and Economides Multiple fractures, analytical  Other similar analytical solutions Levitan  Kuppe & Settari Numerically based correlations  Karcher et al. Numerically derived for single transverse fracture  Mukherjee and Economides Multiple fractures, analytical  Other similar analytical solutions Levitan  Kuppe & Settari Numerically based correlations

13. Analytical Methods - fractured horiz well  Mukherjee & Economides - based on linear flow, applicable to multiple fracs, but neglects frac interaction  Karcher et al - more realistic, based on simulation, but only for single frac and one thickness  Mukherjee & Economides - based on linear flow, applicable to multiple fracs, but neglects frac interaction  Karcher et al - more realistic, based on simulation, but only for single frac and one thickness

14. Evaluation of Analytical methods  Single Transverse, Fully Penetrating, Static Fracture: Effect of Dimensionless Length and Reservoir Thickness on Productivity  Reference solution generated by finely gridded simulator  Single Transverse, Fully Penetrating, Static Fracture: Effect of Dimensionless Length and Reservoir Thickness on Productivity  Reference solution generated by finely gridded simulator x fD = x f /L

15. Single Transverse, Fully Penetrating, Static Fracture Effect of Length and Reservoir Thickness on Productivity (Numerical and Karcher et al.)

16. Single, Transverse, Fully Penetrating Static Fracture Errors in Analytical Approximations Numerical vs. Mukherjee(sp?) and Economides, for Constant Pressure Boundary Condition

17. Conclusions: Analytical methods for fractured horizontal well  Karcher method reasonable, but derived only for one reservoir thickness  M&E fails to preserve true character (results linear with x fd ) - not recommended. Same applies to multi-frac version of M&E  Karcher method reasonable, but derived only for one reservoir thickness  M&E fails to preserve true character (results linear with x fd ) - not recommended. Same applies to multi-frac version of M&E

18. 3. Multiple Static, Fully Penetrating, Transverse Fractures in a Finite Drainage Area

19. Kuppe’s Method (JCPT, 1998):  Data were generated from detailed simulations  Numerical model allows full anisotropy, partial penetration, turbulence, finite conductivity...  Analytical Correlations were developed for: 1, 3, 5 and 7 fractures fully penetrating, infinite conductivity fractures closed boundary (pseudo-steady state conditions), k x =k y =k z =k= 1,10, 50, 100 md single phase Darcy flow  Data were generated from detailed simulations  Numerical model allows full anisotropy, partial penetration, turbulence, finite conductivity...  Analytical Correlations were developed for: 1, 3, 5 and 7 fractures fully penetrating, infinite conductivity fractures closed boundary (pseudo-steady state conditions), k x =k y =k z =k= 1,10, 50, 100 md single phase Darcy flow

20. Example of Using Kuppe’s Method: Correlation for 50 md 1 2 3 4 5 6 7 8 9 10 0.000.100.200.300.400.500.600.700.800.901.00 Dimensionless Fracture Half Length Productivity Index ratio (Fractured/unfractured) 7 fracs 5 fracs 3 fracs 1 frac

21. Numerical Modeling

22. Fractured Horizontal Wells With Static Fractures (Clean Water)  Not routine in most simulators Requires fine gridding around the fractures and around the well This results in slow running models  For PWRI: Stress-dependent fracture conductivity is favourable Turbulence may be a significant issue even for water Simulation of reopening or closure of fractures requires coupled geomechanics Plugging not included in most simulators  Not routine in most simulators Requires fine gridding around the fractures and around the well This results in slow running models  For PWRI: Stress-dependent fracture conductivity is favourable Turbulence may be a significant issue even for water Simulation of reopening or closure of fractures requires coupled geomechanics Plugging not included in most simulators

23. 4. Growth of Dynamic Fractures from horizontal injectors  Issues: Initiation locations (in OH, SL completions) Competiton between fracs Vertical growth and layered formations  Issues: Initiation locations (in OH, SL completions) Competiton between fracs Vertical growth and layered formations

24. Forecasting Growth of Dynamic Fractures  Most work has been done on vertical wells (full perforation height) and single fracture without plugging Analytical methods Numerical methods  There are important specific issues affecting injectivity for horizontal wells  Most work has been done on vertical wells (full perforation height) and single fracture without plugging Analytical methods Numerical methods  There are important specific issues affecting injectivity for horizontal wells

25. Analytical Methods

26. Dynamic Fractures: Analytical Methods  Carter  Hagoort, Koning  Perkins & Gonzales, Detienne  Owens & Niko, later Shell models  All of the above are for a single fracture, many for 2-D frac geometry (constant height)  Carter  Hagoort, Koning  Perkins & Gonzales, Detienne  Owens & Niko, later Shell models  All of the above are for a single fracture, many for 2-D frac geometry (constant height)

27. Numerical Methods

28.  Models specific to water injection: Hagoort, Weatherill, Settari (1980) Nghiem, Jensen BP (Clifford-BPOPE), Shell models  Adapted general fracturing models: DE&S waterflood version of STRESSFRAC TerraFrac - plugging can be added - can handle inclined well Perkins (cake deposition)  Most above are for a single vertical fracture, usually for a vertical well or approximate horiz well by limited perforated length  Models specific to water injection: Hagoort, Weatherill, Settari (1980) Nghiem, Jensen BP (Clifford-BPOPE), Shell models  Adapted general fracturing models: DE&S waterflood version of STRESSFRAC TerraFrac - plugging can be added - can handle inclined well Perkins (cake deposition)  Most above are for a single vertical fracture, usually for a vertical well or approximate horiz well by limited perforated length

29. Differences Between Numerical Models  Fracture geometry calculation: 2-D or 3-D fracture mechanics, analytical or numerical simplified (pressure or stress dependent transmissibility) directional joint reopening  Coupling with reservoir flow: classical leakoff models (majority) numerical 1-D modeling (e.g., STRESSFRAC) fully coupled (e.g., BPOPE, GEOSIM)  Fracture geometry calculation: 2-D or 3-D fracture mechanics, analytical or numerical simplified (pressure or stress dependent transmissibility) directional joint reopening  Coupling with reservoir flow: classical leakoff models (majority) numerical 1-D modeling (e.g., STRESSFRAC) fully coupled (e.g., BPOPE, GEOSIM)

30. Competition between Multiple Fractures  Siriwardane (1994) Considered coupling between the pressure drop in the well between fractures and the net pressure in each fracture Analysis was done for CGD fracture geometry only Solves a nonlinear set of equations and constraints Results are prejudiced by the choice of the geometry (which dictates the net pressure vs. length signature)  Siriwardane (1994) Considered coupling between the pressure drop in the well between fractures and the net pressure in each fracture Analysis was done for CGD fracture geometry only Solves a nonlinear set of equations and constraints Results are prejudiced by the choice of the geometry (which dictates the net pressure vs. length signature)

31. Competition between Multiple Fractures  Siriwardane (1994) The choice of the CGD geometry dictates that net pressure decreases with fracture length:  Siriwardane (1994) The choice of the CGD geometry dictates that net pressure decreases with fracture length:

32. Dynamic Multiple Fracture Growth: Siriwardane Method  Illustrates possibility of very uneven growth of simultaneous parallel fractures  Frac length is determined by p f =f(X f ) relation; pf difference between cracks = f(wellbore friction)  Results depend on assumed net pressure model (i.e., a fracture further from the heel with a lower p w grows faster because of the decreasing p f vs X f model)  Method needs to be coupled with more realistic (3-D) net pressure generator to be useful  Illustrates possibility of very uneven growth of simultaneous parallel fractures  Frac length is determined by p f =f(X f ) relation; pf difference between cracks = f(wellbore friction)  Results depend on assumed net pressure model (i.e., a fracture further from the heel with a lower p w grows faster because of the decreasing p f vs X f model)  Method needs to be coupled with more realistic (3-D) net pressure generator to be useful

33. Interaction of Fractures due to well friction

36. Dynamic Multiple Fracture Growth: Numerical Methods  BPOPE - SPE 59354: recent enhancements - possibility of modeling growth of simultaneous parallel fractures  Coupling with thermal wellbore calculations is important for inejction profile control (split between fracs)  GEOSIM - simplified method of modeling farc mechanics, allows any number of fracs to propagate, no wellbore calculations currently  Other models?  BPOPE - SPE 59354: recent enhancements - possibility of modeling growth of simultaneous parallel fractures  Coupling with thermal wellbore calculations is important for inejction profile control (split between fracs)  GEOSIM - simplified method of modeling farc mechanics, allows any number of fracs to propagate, no wellbore calculations currently  Other models?

37. 5. Injectivity of high angle wells (arbitrary trajectory)  Most difficult to analyze

38. Injectivity of high angle wells  Analytical methods 4Lee ? 4Xx and Dusseault 4xxx (CIM paper 4Levitan (BP, unpublished) 4Other (plse contribute)  Need to be compared  Most not for layered formations, fairly complex to apply  No plugging physics  Analytical methods 4Lee ? 4Xx and Dusseault 4xxx (CIM paper 4Levitan (BP, unpublished) 4Other (plse contribute)  Need to be compared  Most not for layered formations, fairly complex to apply  No plugging physics

39. Injectivity of high angle wells  Numerical methods 4Difficult gridding problem - grid should conform to layering AND well trajectory 4Problem to correctly model anisotropy with arbitrary grids 4Crossflow 4Results in difficult to set up, fine-grid, slow running models  PWRI plugging not included  Need for an alternative - specialized quick- evaluation tool  Numerical methods 4Difficult gridding problem - grid should conform to layering AND well trajectory 4Problem to correctly model anisotropy with arbitrary grids 4Crossflow 4Results in difficult to set up, fine-grid, slow running models  PWRI plugging not included  Need for an alternative - specialized quick- evaluation tool

40. 6. Other Issues and Mechanisms Specific to Fractures in Horizontal Wells:  Entrance region of the fracture (added resistance - lower II)  Possible turbulence effects (recent DE&S work with Statoil) - extension of Europec 94 paper  Competition between fracs influenced by poroelastic and thermal stresses  Not included in any analytical models surveyed  Can be represented in some numerical models  Entrance region of the fracture (added resistance - lower II)  Possible turbulence effects (recent DE&S work with Statoil) - extension of Europec 94 paper  Competition between fracs influenced by poroelastic and thermal stresses  Not included in any analytical models surveyed  Can be represented in some numerical models

41. Effect of Turbulence on Injectivity of Fractured Horizontal Wells:  Analytical method of Guppy (1982) for vertical wells does not account for convergence to the wellbore  Numerical solutions show that turbulence is primarily confined to the fracture and can have a large effect (two orders of magnitude) even for liquid flow  Benefit of fracturing can be significantly reduced at high rates  Possibility to create multiple fractures by this mechanism (similar to limited entry)? - HYPOTHESIS ONLY  Analytical method of Guppy (1982) for vertical wells does not account for convergence to the wellbore  Numerical solutions show that turbulence is primarily confined to the fracture and can have a large effect (two orders of magnitude) even for liquid flow  Benefit of fracturing can be significantly reduced at high rates  Possibility to create multiple fractures by this mechanism (similar to limited entry)? - HYPOTHESIS ONLY

42. Factors controlling PI reduction due to turbulence:  For fully penetrating vertical fracture in vertical well: Dimensionless injection rate Frac dimensionless conductivity F cD One Dimensional parameter (C f, W f or X f ) Permeability  Note: for the same F cD, fracture with larger width (vs perm) will have lower turbulence (FracPack)  For partial perforation Dimensionless perf height  Horizontal well with transverse fracture behaves as a vertical well with EXTREMELY small perforation height (fracture contribution only)  For fully penetrating vertical fracture in vertical well: Dimensionless injection rate Frac dimensionless conductivity F cD One Dimensional parameter (C f, W f or X f ) Permeability  Note: for the same F cD, fracture with larger width (vs perm) will have lower turbulence (FracPack)  For partial perforation Dimensionless perf height  Horizontal well with transverse fracture behaves as a vertical well with EXTREMELY small perforation height (fracture contribution only)

43. Horiz. well

44. Recommendations for Selecting an Appropriate Calculation Method:

45.  Be careful with simple analytical methods  In back analysis, if discrepancies occur: consider other factors (conformance, fracture growth, turbulence, damage … ) may need simulation analysis  In design, use the simplest tool which captures the intended design features  Need to develop simple method to account for plugging and heterogeneity (layering)  Be careful with simple analytical methods  In back analysis, if discrepancies occur: consider other factors (conformance, fracture growth, turbulence, damage … ) may need simulation analysis  In design, use the simplest tool which captures the intended design features  Need to develop simple method to account for plugging and heterogeneity (layering)