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IMPACT OF TRANSMISSIBILITY CORRECTIONS ON SHALE GAS NUMERICAL PRODUCTION FORECASTS

IMPACT OF TRANSMISSIBILITY CORRECTIONS ON SHALE GAS NUMERICAL PRODUCTION FORECASTS. Context. Typical analysis workflow involves a step from analytical to numerical models Objective: ensure consistency between models

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IMPACT OF TRANSMISSIBILITY CORRECTIONS ON SHALE GAS NUMERICAL PRODUCTION FORECASTS

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  1. IMPACT OF TRANSMISSIBILITY CORRECTIONS ON SHALE GAS NUMERICAL PRODUCTION FORECASTS

  2. Context • Typical analysis workflow involves a step from analytical to numerical models • Objective: ensure consistency between models • Low permeability context induces specific complexity for numerical simulation

  3. Reference solution • Transient models for hydraulic fractures for monophasic, linear PVT based on: • Ozkan, E. and Raghavan, R.: “New Solutions for Well-Test Analysis Problems: Part 1 – Analytical Considerations,” SPEFE (Sept. 1991).

  4. Observations

  5. Observations k=30 mD

  6. Observations k=30 mD

  7. Observations k=1E-4 mD Grid size cannot be set irrespectively of k for transient analysis

  8. Observations k=1E-4 mD Linear transmissibilities overestimate production

  9. Non-Linear PVT Gas: PVT non-linearity increases the productivity

  10. Observations • In low-permeability formations, numerical results show specific behavior • Transmissibility values must be corrected to account for NL pressure behavior • Grid size must be carefully chosen to capture transients • Grid size should also capture PVT non-linearity

  11. Transmissibility corrections Linear assumption:

  12. Transmissibility corrections Cell average pressure : Darcy’s law : General expression:

  13. Transmissibility corrections • Analytical pressure field obtained from successive integrations of source point solutions • Numerical volume and surface integrations on every cell geometry

  14. Transmissibility corrections Unitary panel solution Weight First images solution • Weights are either: • set to equate potential at a number of locations along the producing surfaces (iso-potential surfaces), a linear system has to be solved (once for a given geometry). • set equals (uniform flux).

  15. Transmissibility corrections Potential field around a partially penetrating slanted well in a single layer.

  16. Numerical examples Example 1: single, fully penetrating fracture

  17. Numerical examples Isopotentiallines and corresponding truncated numerical grid.

  18. Numerical examples

  19. Numerical examples Cumulative production error compared to reference solution

  20. Numerical examples Example 2: MFHW with fully penetrating fractures

  21. Numerical examples

  22. Numerical examples Cumulative production error compared to reference solution

  23. Numerical examples Example 3: single, partially penetrating fracture

  24. Numerical examples

  25. Numerical examples Cumulative production error compared to reference solution

  26. Numerical examples Example 4: MFHW, partially penetrating fractures

  27. Numerical examples Example 4: MFHW, partially penetrating fractures

  28. Numerical examples

  29. Numerical examples Cumulative production error compared to reference solution

  30. Grid Refinement Control MFHW with 30 Fractures, k=1E-4 mD

  31. Grid Refinement Control • Objective: automatic choice of the grid refinement based on the desired time resolution • Effective resolution is related to the radius of investigation:

  32. Grid Refinement Control Constant PVT

  33. Grid Refinement Control NL gas PVT : slightly smaller effective resolution with large P

  34. Conclusions • Specific procedures have been developed for low-k • Transmissibility corrections Reduce numerical errors with large NL pressure effects • Corrections valid only for kfractures >> kreservoir • Automatic grid refinement procedure Based on estimated radius of investigation at desired time resolution

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