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Analysis of Layered Gas Reservoir Performance Using a Quasi-Analytical Solution for

Analysis of Layered Gas Reservoir Performance Using a Quasi-Analytical Solution for Rate and Pressure Behavior. I Nengah Suabdi. Department of Petroleum Engineering Texas A & M University 9 May 2001. Outline. Introduction Objectives Assumptions Semi-analytical solutions

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Analysis of Layered Gas Reservoir Performance Using a Quasi-Analytical Solution for

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  1. Analysis of Layered Gas Reservoir Performance Using a Quasi-Analytical Solution for Rate and Pressure Behavior I Nengah Suabdi Department of Petroleum Engineering Texas A & M University 9 May 2001

  2. Outline • Introduction • Objectives • Assumptions • Semi-analytical solutions • New Type Curves for Layered Gas Reservoirs • Field Application • Conclusions

  3. Single Layer or Equivalent Single Layer Model Introduction No-Crossflow Depletion Performance Analysis: • Is a single layer model satisfactory..? Layer-1 Single layer model..? where : k1>k2 ..? • Can single-layer model performance detect layering..? , layer volume..?, or effect of drawdown..? Layer-2 Layered-gas reservoir depletion study: • Fetkovich, M.J. et.al (1990) • Using numerical simulations

  4. Objectives 1. To provide a quasi-analitycal solution for the depletion performance of a well produced at a common production pressure in a layered gas reservoir. 2. To utilize this quasi-analytical gas flow solution as a mechanism for charac-terizing the performance of layered gas reservoirs.

  5. Objectives The proposed analysis techniques will be used to estimate the following properties for a layered gas reservoir system: • The permeability ratio (2-layer case). • Layer productivity index (Jg) • The total original gas-in-place (G). • The total flow capacity (kh product). • The moveable reserves in each layer.

  6. Schematic diagram of layered reservoir Layer-1 Layer- 2 Layer- 3 Layer- n

  7. No-Crossflow Production is commingled Physical Model Gas Reservoir k1 h1 Layer-1 k2 h2 Layer-2 Assumptions:  Two-layer (dry) gas reservoir  No crossflow in the reservoir  Homogeneous (except klayer)  Bounded radial system (pseudosteady-state flow)  Production is commingled at a constant BHP

  8. is not constant because µ and ct are functions of pressure Gas Diffusivity Equation in terms of :pressure (p), pseudopressure (pp), and time :

  9. Plot of the Viscosity-Compressibility Function(Ansah et.al)

  10. Semi-Analytical Solutions We consider the "first-order polynomialmodel" for correlating the curves. This result is given by Ansah, et al. as: We can then develop the dimensionless decline rate (qDd), pressure (pD), and cumulative production (GpD).

  11. Semi-Analytical Solutions The fundamental form of stabilizedflow equation is given by Where :

  12. Semi-Analytical Solutions Gas MBE for moderate to low pressure reservoirs: Where the dimensionless pressures are defined by:

  13. Semi-Analytical Solutions • Dimensionless Pressure (pD) Where :

  14. Semi-Analytical Solutions • Dimensionless Decline Rate (qDd) Where :

  15. Semi-Analytical Solutions • Dimensionless Cumulative Production (GpD) Where :

  16. Semi-Analytical Solutions • In field units, the dimensionless "decline" time is defined as: Where : t = Time, days kj= Permeability ( layer j), md fj = Porosity ( layer j), fraction cti = Total system compressibility, psia-1 re= Radius of the external boundary, ft

  17. Semi-Analytical Solutions • Gas rate production for each layer (qgj) in-term of (p/z)2 is defined as Where : Cj = Stabilized flow coefficient layer-j, Mscf/D/psi2 kj= Permeability ( layer j ), md fj = Porosity ( layer j ), fraction cti = Total system compressibility, psi-1 pref= (pi + pwf)/2, psi

  18. Pressure Depletion Decline Type Curve

  19. Pressure Depletion Decline Type Curve

  20. Pressure Depletion Decline Type Curve

  21. Pressure Depletion Decline Type Curve

  22. Pressure Depletion Decline Type Curve Vol Layer-1 Vol Layer-2 pwD = 0.1 G

  23. Pressure Depletion Decline Type Curve pwD=0.2 G

  24. Pressure Depletion Decline Type Curve pwD=0.3 G

  25. Pressure Depletion Decline Type Curve pwD=0.4 G

  26. Pressure Depletion Decline Type Curve pwD=0.5 G

  27. Depletion Decline Rate Type Curve

  28. Rate Depletion Decline Type Curve

  29. Rate Depletion Decline Type Curve

  30. Rate Depletion Decline Type Curve

  31. Rate Depletion Decline Type Curve

  32. GpD vs. Dimensionless Decline Time (tDd)

  33. Stabilized Gas Flow Coefficient (cj)

  34. p/z vs GpD,t Function

  35. Field Application (p/z vs. GptCurve Example) • Well Beavers 1-11 (Hugoton Field, Kansas, USA)

  36. Field Application (p/z vs. GptCurve Example) • Well Beavers 1-11 (Hugoton Field, Kansas, USA)

  37. Field Application (p/z vs. GptCurve Example) • Well Beavers 1-11 (Hugoton Field, Kansas, USA)

  38. Field Application (p/z vs. GptCurve Example) • Well Beavers 1-11 (Hugoton Field, Kansas, USA)

  39. G = 24.11 BSCF p/z versus Gpt —Cartesian format. • Well Beavers 1-11 (Hugoton Field, Kansas, USA) Less Permeable Layer More Permeable Layer

  40. qg versus prod time —semilog format. • Well Beavers 1-11 (Hugoton Field, Kansas, USA)

  41. qg versus prod time —log-log format. • Well Beavers 1-11 (Hugoton Field, Kansas, USA)

  42. Gptversus prod time —semilog format. • Well Beavers 1-11 (Hugoton Field, Kansas, USA)

  43. Gptversus prod time —log-log format. • Well Beavers 1-11 (Hugoton Field, Kansas, USA)

  44. Estimate properties of Well Beavers 1-11 - Total original gas-in-place (G) = 24.11 BSCF - The permeability ratio (k1/k2) = 68 - Total reservoir thickness, (htot) = 130 ft - Average reservoir radius, (re) = 3,250 ft - Average area each layer, (Aavg) = 761.76 Acres - The total flow capacity, (kh product) = 482 md-ft - The magnitude of wellbore F. Press (Pwf) = 20 psia

  45. Field Application (Rate typeCurve Example) • Nelson well (Hugoton Field, Kansas (USA)) MP

  46. Field Application (Rate typeCurve Example) • Gas Well- B

  47. Conclusions 1.We successfully demonstrated the use of a semi-analytical solution for a single-layer gas system for layered gas reservoir cases presented by Fetkovich, et.al (numerical simulations). 2.A two-layer type curve was developed for the analysis of production performance. The single- layer case can not be used to model the 2-layer case. 3. The sensitivity of individual layer properties was investigated, in particular — permeability ratio, layer volumes, and the effect of drawdown.

  48. Analysis of Layered Gas Reservoir Using Production Data I Nengah Suabdi Department of Petroleum Engineering Texas A & M University 3 February 2001

  49. Field Application (Example) • Curtis well (Hugoton Field, Kansas, USA) Less Permeable Layer

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