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- 1. Determining OGIP and Aquifer Performance With No Prior Knowledge of Aquifer Properties and Geometry Leonardo Vega Texas A&M University Masters’ Division SPE International Student Paper Contest October 5, 1999
- 2. New Approach <ul><li>OGIP </li></ul><ul><li>Aquifer Performance </li></ul><ul><li>No Prior Knowledge of Aquifer Properties or Geometry are Required </li></ul><ul><li>Only Production Performance Data </li></ul>© Leonardo Vega
- 3. <ul><li>Previous methods require a lot of information about the aquifer </li></ul><ul><li>Previous methods require a homogeneous aquifer </li></ul><ul><li>New method is very practical </li></ul><ul><li>Other methods are very idealistic </li></ul>Advantages of New Method
- 4. Overview of Presentation <ul><li>Introduction </li></ul><ul><li>Previous Methods </li></ul><ul><li>New Approach </li></ul><ul><li>Results </li></ul><ul><li>Conclusions </li></ul>© Leonardo Vega
- 5. Overview of Presentation <ul><li>Introduction </li></ul><ul><li>Previous Methods </li></ul><ul><li>New Approach </li></ul><ul><li>Results </li></ul><ul><li>Conclusions </li></ul>© Leonardo Vega
- 6. Material Balance Water drive Strong Moderate 0 p i /z i 0 G p =G p/Z G p Depletion
- 7. Performance of Water-Drive Gas Reservoirs Is Rate-Dependent 2,500 2,700 2,900 3,100 3,300 3,500 3,700 0 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000 G p G p , MMscf p/z © Leonardo Vega 0 100 200 300 400 500 600 Gas Rate, MMscf/Day
- 8. p/Z Plot of Water-Drive Gas Reservoir May Look Linear p 2 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 OGIP G p , Bscf p/z psia
- 9. Overview of Presentation <ul><li>Introduction </li></ul><ul><li>Previous Methods </li></ul><ul><li>New Approach </li></ul><ul><li>Results </li></ul><ul><li>Conclusions </li></ul>© Leonardo Vega
- 10. In 1949, van Everdingen-Hurst Presented Solution to Diffusivity Equation <ul><li>Aquifer Homogeneity </li></ul>© Leonardo Vega <ul><li>Elementary Reservoir-Aquifer Geometries </li></ul>Aquifer Gas Reservoir
- 11. In 1964-65 Havlena-Odeh presented Technique for Aquifer Fitting © Leonardo Vega F/E g (Bscf) W e B w /E g (Bscf) Aquifer too small Aquifer too large Correct Match 45 o G
- 12. Technique of Havlena-Odeh Lacks Uniqueness F/E g (Bscf) W e B w /E g (Bscf) © Leonardo Vega Aquifer Description 2 Aquifer Description 1 G 1 G 2
- 13. Definition of Aquifer Influence Functions (AIF) <ul><li>Pressure drop due to a unit water influx rate at the original GWC </li></ul><ul><ul><li>like type curves </li></ul></ul><ul><ul><li>unique to each aquifer </li></ul></ul>© Leonardo Vega
- 14. In 1964, Coats et al. Presented an Aquifer Model <ul><li>Systems of Arbitrary Geometry and Heterogeneity </li></ul><ul><li>They Proposed The Use AIF </li></ul>Aquifer Gas Reservoir © Leonardo Vega
- 15. Coats et al. ’s Exact Solution © Leonardo Vega
- 16. In 1988, Gajdica Proposed New Method <ul><li>Calculated OGIP and aquifer performance from production performance data </li></ul><ul><li>Used linear programming technique </li></ul><ul><li>Used 32 field data sets to validate results </li></ul>© Leonardo Vega
- 17. Gajdica’s Technique
- 18. Gajdica’s Technique Had Problems OGIP, Bscf Relative Error, psi/Bscf © Leonardo Vega G p max G opt 0 200 400 600 800 1000 1200 1400 0 2 4 6 8 10 12
- 19. Two Questions Arise About Use of Gajdica’s Technique <ul><li>Is the technique presented by Gajdica valid at all? </li></ul><ul><li>Is the anomaly due to errors in some of his field data? </li></ul>© Leonardo Vega
- 20. Is Gajdica’s Technique Valid At All? <ul><li>The Relative Error Function Lacks any Statistical Meaning </li></ul>© Leonardo Vega
- 21. Overview of Presentation <ul><li>Introduction </li></ul><ul><li>Previous Methods </li></ul><ul><li>New Approach </li></ul><ul><li>Results </li></ul><ul><li>Conclusions </li></ul>© Leonardo Vega
- 22. Absolute Error Function Has Sound Statistical Meaning © Leonardo Vega
- 23. Methodology to Analyze Performance Behavior <ul><li>Analyze the behavior of the Normalized Absolute Error, A N , instead of the Relative Error </li></ul><ul><li>Use synthetic data to isolate the nature of the problem. </li></ul>© Leonardo Vega
- 24. Procedure To Determine OGIP and AIF <ul><li>Assume several values of OGIP. </li></ul><ul><li>Optimize the A N . </li></ul><ul><li>For each assumed OGIP, report the optimized A N , and corresponding AIF. </li></ul><ul><li>Plot the optimized A N versus the assumed OGIP. </li></ul>
- 25. AIF Must Meet Certain Smoothness Constraints © Leonardo Vega <ul><li>The AIF must be positive or zero </li></ul>Aquifer Influence Function 0.0000 6.0000 0 30 t F(t) t
- 26. AIF Must Meet Certain Smoothness Constraints © Leonardo Vega <ul><li>The AIF must increase or remain constant </li></ul>Aquifer Influence Function 0.0000 6.0000 0 30 t F(t) t
- 27. AIF Must Meet Certain Smoothness Constraints © Leonardo Vega <ul><li>The AIF must be concave downward or be a straight line </li></ul>Aquifer Influence Function 0.0000 6.0000 0 30 t F(t) t
- 28. Reservoir Data Assumed to Generate Synthetic Performance © Leonardo Vega
- 29. Volumetric Reservoir Flow Rate and p/Z Performance p 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 0 20,000 40,000 60,000 80,000 100,000 0 10 20 30 40 50 60 70 80 90 100 © Leonardo Vega G p , MMscf
- 30. A N Displayed Typical Behavior In Volumetric Depletion Reservoirs 0 50 100 150 200 250 300 350 0 200 400 600 800 1,000 1,200 0-A : Lower Region A-B : Middle Region Larger than B: Upper Region B A © Leonardo Vega A N , psi/point OGIP, Bscf
- 31. e w Calculated from Material Balance Equation Volumetric Depletion Reservoir For G<G actual e w >0 For G>G actual e w <0 © Leonardo Vega
- 32. For G<G actual (Volumetric Depletion Reservoir)
- 33. Pressure Match When G<G actual (Volumetric Depletion Reservoir) © Leonardo Vega
- 34. A N Behavior for G<G actual (Volumetric Depletion Reservoir) 0 50 100 150 200 250 300 350 0 200 400 600 800 1,000 1,200 A N , psi/point OGIP, Bscf
- 35. For G>G actual (Volumetric Depletion Reservoir) F(t)=0 p cal =0
- 36. For G>G actual (Volumetric Depletion Reservoir) Since p cal =0
- 37. Middle Region (Volumetric Depletion Reservoir) © Leonardo Vega
- 38. Zoomed View of Lower Region (Volumetric Depletion Reservoir) © Leonardo Vega
- 39. Water-Drive Gas Reservoir Aquifer Data Assumed © Leonardo Vega
- 40. Water Drive Gas Reservoir q g =50 MMscf/D 0 10 20 30 40 50 60 200 400 600 800 1,000 G p , MMscf 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 Gas Rate Observed Pressure OGIP overestimated by 39% © Leonardo Vega OGIP actual =700 Bscf
- 41. Behavior of A N Water Drive Gas Reservoir ( q g =50 MMscf/D) © Leonardo Vega
- 42. Zoomed View of A N Water Drive Gas Reservoir ( q g =50 MMscf/D) © Leonardo Vega
- 43. Obtained The Same AIF For All Production Schedules 0.0E+00 1.0E-02 2.0E-02 3.0E-02 4.0E-02 5.0E-02 6.0E-02 0 100 200 300 400 500 600 Time, days © Leonardo Vega
- 44. Overview of Presentation <ul><li>Introduction </li></ul><ul><li>Previous Methods </li></ul><ul><li>New Approach </li></ul><ul><li>Results </li></ul><ul><li>Conclusions </li></ul>© Leonardo Vega
- 45. Performance Data of Field “A” © Leonardo Vega Rate and Pressure Behavior as a function of Gp 0 10 20 30 40 50 60 70 80 90 100 5 10 15 20 25 30 35 G pa , BScf 5,200 5,300 5,400 5,500 5,600 5,700 5,800 5,900 6,000 6,100 Gas Rate Observed p/Z q g , MMscf p/Z, psia
- 46. p/Z Technique 0 10 20 30 40 50 60 70 80 90 100 50 100 150 200 250 300 G pa , BScf 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 Gas Rate Observed q g , MMscf/d p/Z, psia
- 47. OGIP Determined with New Approach © Leonardo Vega 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 100 200 300 A N , psi/point OGIP, Bscf
- 48. Overview of Presentation <ul><li>Introduction </li></ul><ul><li>Previous Methods </li></ul><ul><li>New Approach </li></ul><ul><li>Results </li></ul><ul><li>Conclusions </li></ul>© Leonardo Vega
- 49. Conclusions Unlike the p/z plot, the shape of the A N permits the recognition of the reservoir drive mechanism. The A N allows the determination of the OGIP in a water-drive reservoir. No prior knowledge or assumptions about the aquifer properties and geometry are required . © Leonardo Vega
- 50. Conclusions The optimum OGIP is located where the middle and the lower regions coincide. The drive mechanism and the optimum OGIP can be easily recognized, even when few production-pressure data are available. © Leonardo Vega
- 51. Conclusions Even though the risk of a non-unique solution exists, its occurrence has been diminished. Unlike the Havlena-Odeh method, when used along with the the van EverdingenHurst exact solution, this method does not need a continuous re-evaluation of the aquifer. © Leonardo Vega
- 52. Determining OGIP and Aquifer Performance With No Prior Knowledge of Aquifer Properties and Geometry Leonardo Vega Texas A&M University Masters’ Division SPE International Student Paper Contest October 5, 1999
- 53. Volumetric Gas Reservoirs No Water Encroachment © Leonardo Vega
- 54. How to Generate Synthetic Data <ul><li>Assume aquifer geometry. </li></ul><ul><li>Assume k, , , c t , A, and x e in aquifer. </li></ul><ul><li>Assume reservoir properties T, g , c f , c w , G and p i .. </li></ul><ul><li>Calculate z, B g , B w , and V p . </li></ul><ul><li>Assume q g (t) and calculate G p . </li></ul><ul><li>Calculate p D (t D ) from exact solution of Diffusivity Equation. </li></ul>
- 55. <ul><li>Calculate p(t) using the Superposition Principle. </li></ul><ul><li>Use t, p(t) and DG p (t) as input to the AIF program (Reservoir Performance Data). </li></ul>How to Generate Synthetic Data
- 56. Water Drive Gas Reservoir q g =100 MMscf/D © Leonardo Vega
- 57. A N Behavior Water Drive Gas Reservoir ( q g =100 MMscf/D) © Leonardo Vega
- 58. Water Drive Gas Reservoir q g =150 MMscf/D © Leonardo Vega
- 59. A N Behavior Water Drive Gas Reservoir (q g =150 MMscf/D) © Leonardo Vega
- 60. Water Drive Gas Reservoir Variable Production Rate OGIP overestimated by 32% © Leonardo Vega
- 61. A N Behavior Water Drive Gas Reservoir (Variable Production Rate) © Leonardo Vega
- 62. A N Behavior (Zoomed View) Water Drive Gas Reservoir (Variable Production Rate) © Leonardo Vega
- 63. Limitations © Leonardo Vega
- 64. Limitations © Leonardo Vega

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