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Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs

Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs. Taufan Marhaendrajana Ph.D. Candidate Texas A&M University. SPE International Paper Contest 5 October 1999. 10 Second Summary.

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Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs

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  1. Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs Taufan Marhaendrajana Ph.D. Candidate Texas A&M University SPE International Paper Contest 5 October 1999

  2. 10 Second Summary • Developed a new method to estimate the original oil/gas-in-place by analyzing production data from only one well. • This method can also be used to esti-mate the permeability-thickness product in the drainage area for a particular well. • These developments are based on an analytical solution for a multiwell model.

  3. Why is this work important? Multiwell Solution  Accurate Rigorous and robust  Very fast solution (can be run on a PC) Multiwell Analysis Approach  Can be based on single-well decline type curve  "Total Material Balance Time"  system volume Easy-to-apply Validation  Homogeneous reservoir case  Heterogeneous reservoir case Field Cases (Arun Gas Field, Indonesia)

  4. Outline • Introduction • Objectives • Physical Model and Analytical Solution • Decline Type Curve Analysis • Field Application (Arun Field, Indonesia) • Conclusions • Recommendations for Extensions of This Work

  5. Introduction Current Multiwell Models • Rodriguez and Cinco-Ley (1993) • Camacho et al (1996) • Constant pressure only • Pseudosteady-state only • Does notprovide a mechanism for analyzing production data Current Multiwell Models • Valko et al (1998) • Pseudosteady-state only • Does notprovide a mechanism for analyzing production data Production Data Analysis? Modeling of Individual Well Performance?  Single Well Model (Well-by-well analysis) • Is a single well model satis-factory? Bounded Reservoir with Multiple Wells

  6. Objectives 1. To Develop an Analytical Solution for a Single Well or Multiple Wells in a Multiwell Reservoir System • Correctly models all flow regimes. • Completely general formulation (constant rate, constant pressure, or variable-rate/pressure). 2. To Develop a Method for the Analysis of Production Data from a Multiwell System • Estimate the originaloil/gas-in-place. • Estimate the local flow capacity (permeability-thickness product).

  7. Physical Model (0,0,0) xe ye ze Assumptions: Homogeneous, Closed Reservoir  Slightly Compressible Fluid  Fully Penetrating Wells

  8. Well Pressure Solution (Convolution Form) • Accuracy • Speed • Formulation Constant Rate Solution For Single Well in A Closed Rectangular Reservoir i = well counter k = well index (well location where pressure is evaluated)

  9. Numerical Simulation Model (Base Case) Initial Pressure : 5,000 psi Permeability : 5 md Porosity : 0.2 Total Comp. : 3x10-6 1/psia Thickness : 500 ft Area : 16,8602 ft2 No. of Wells : Nine Oil Viscosity : 0.8 cp FVF : 1.184 RB/STB OOIP : 4,278MMSTB [3,1] [3,2] [3,3] Permeability : 5 md [2,3] [2,1] [2,2] [1,1] [1,2] [1,3] OOIP : 4,278 MMSTB

  10. Well [1,3] Well [1,1] Well [1,2] Well [2,1] Well [2,2] Well [2,3] Bottom Hole Flowing Pressure, psi Well [3,1] Well [3,2] Well [3,3] Time, Days

  11. Well [1,1] Well [1,2] Well [1,3] Well [2,2] Well [2,3] Well [2,1] Oil Rate, STB/D Well [3,3] Well [3,1] Well [3,2] Time, Days

  12. Analytical Solution Matches Numerical Solution Initial pwf Variable pwf Final pwf Oil Rate, STB/D Well [1,2] Time, Days

  13. Decline Type Curve Analysis • Formulation for Multiwell Decline Type Curve Analysis • Fetkovich/McCray Decline Type Curve • Decline Type Curve Analysis Procedure • Application to Simulated Performance Data

  14. Formulation for Multiwell Analysisusing Decline Type Curves vs c(t) c(t) Production Data (Pressure & Rate) c(t) includes: -Transient flow -Reservoir shape -Well location c(t) becomes constant at long times Total Material Balance Time Original-Oil-in-Place

  15. Type Curve Construction(Multiwell System) bD=1 bD=9 bD=25  

  16. "Total Material Balance Time" Generalizes The Fetkovich/McCray Type Curve 12 7 4 7 4 12 28 18 80 48 800 160 1x104 qDdei 80 48 28 18 12 7 4 Dimensionless Rate Functions (qDde, qDdei, qDdeid) 160 800 qDdeid qDde Dimensionless Total Material Balance Time, tDde,bar

  17. Decline Type Curve Analysis Procedure Log-log Plot Model (Dimensionless Variables) Data qwell/Dpwell tbar,tot=Np,field/qwell Match Original Oil/Gas-In-Place (N or G)  Flow Capacity (kh)

  18. All Curves Overlay Each Other(Homogeneous Reservoir Example) (q/Dp)idis affected by severe rate changes (unlikely in practice) q/Dp, (q/Dp)i, (q/Dp)id, STB/D/psi tbar,tot = Np,field/qwell, Days

  19. 12 7 4 7 4 12 28 18 80 48 800 160 Dimensionless Rate Functions (qDde, qDdei, qDdeid) 1x104 80 48 28 18 12 7 4 160 800 Dimensionless Material Balance Time, tDd,bar or Dimensionless Total Material Balance Time, tDde,bar Multiwell Model Is More Accurate Than Single Well Model Total material balance functions align with correct solution Dimensionless Material Balance Time, tDd,bar Dimensionless Total Material Balance Time, tDde,bar

  20. Locally Homogeneous Reservoir Example Issues: Can we analyze multiwell performance? Accuracy of results?  In-place volume kh-product Uniqueness of the analysis? [ 20 mD ] [ 15 mD ] [ 10 mD ] [ 25 mD ] [ 5 mD ]

  21. Well [1,1] Well [1,2] Well [1,3] Well [2,2] Well [2,3] Well [2,1] Bottom Hole Flowing Pressure, psi Well [3,3] Well [3,1] Well [3,2] Time, Days

  22. Well [1,1] Well [1,2] Well [1,3] Well [2,2] Well [2,3] Well [2,1] Oil Rate, STB/D Well [3,3] Well [3,1] Well [3,2] Time, Days

  23. All Curves Converge to A Single Material Balance Trend DecreasingPermeability Material Balance Trend q/Dp, STB/D/psi tbar,tot = Np,field/qwell, Days

  24. 12 7 4 7 4 12 28 18 80 48 800 160 1x104 80 48 28 18 12 7 4 160 800 Locally Homogeneous Reservoir Example Dimensionless Rate Functions (qDde, qDdei, qDdeid) Dimensionless Total Material Balance Time, tDde,bar

  25. [3,2] [3,3] [3,1] [ 20 mD ] [2,3] [2,2] [2,1] [ 15 mD ] [1,1] [1,2] [1,3] [ 10 mD ] [ 25 mD ] [ 5 mD ] k,calc. (md) k,input (md) Well [1,1] 22.7 22.7 25 5.0 [1,2] 5.15 [1,3] 10 10.1 5.0 [2,1] 5.15 10 [2,2] 9.77 9.77 15 [2,3] 13.8 10 [3,1] 9.94 15 14.2 [3,2] 20 18.9 [3,3] 18.9 OOIP (Input) 4,278 MMSTB OOIP (Calc.) 4,278 MMSTB

  26. Field Application • Description/Layout of Arun Gas Field • Analysis of Production Data (13 Wells) • Comparison with Previous Results

  27. N Arun Field Field Description • Located in Northern part of Sumatra, Indonesia • Retrograde gas reservoir • One of the largest gas fields in the world • Arun Field has 111 wells: • 79 producers • 11 injectors • 4 observation wells • 17 wells have been abandoned Arun Well A-015 Arun Well A-016

  28. Wellhead Pressure Gas (Total Well Stream) Rate, Mscf/D Wellhead Pressure, psi Gas Rate Time, Days Well Performance Data: Arun Well A-015

  29. 12 7 4 7 4 12 28 18 80 48 800 160 1x104 80 48 28 18 12 7 4 160 800 Type Curve Match: Arun Well A-015(Excellent Match of Data/Type Curve) Dimensionless Rate Functions (qDde, qDdei, qDdeid) Transition Boundary Dominated Flow Transient Flow Dimensionless Total Material Balance Time, tDde,bar

  30. Wellhead Pressure Gas (Total Well Stream) Rate, Mscf/D Wellhead Pressure, psi Gas Rate Time, Days Well Performance Data: Arun Well A-016

  31. 12 7 4 7 4 12 28 18 80 48 800 160 1x104 80 48 28 18 12 7 4 160 800 Type Curve Match: Arun Well A-016(Excellent Match of Data/Type Curve) Dimensionless Rate Functions (qDde, qDdei, qDdeid) Transition Boundary Dominated Flow Transient Flow Dimensionless Total Material Balance Time, tDde,bar

  32. Results of Multiwell Analysis at Arun Field Reservoir OGIP (TCF) JPT (June 1983) This Study Numerical Sim. Cumulative Production (Nov. 1998) Flow Capacity (md-ft) Well 912 Arun A-015 19.8 17.1 16.1 ? 996 Arun A-016 Production History: (As of November 1998) • Cumulative gas production (gross) = 21.3 TCF • Cumulative gas reinjected = 5.2 TCF • Net cumulative gas production = 21.3-5.2 = 16.1 TCF • Current monthly gas production = 50 BCF (0.6 TCF/yr) Difference

  33. Material BalanceTrend for Arun Gas Field (OGIP=19.8 TCF) All Cases Converge to A Single Material Balance Trend (Arun Field Data) q/Dp, STB/D/psi tbar,tot = Gp,field/qwell, Days

  34. Type Curve Match: Arun Field--13 Wells(Excellent Match of Data/Type Curve) Dimensionless Rate Functions (qDde, qDdei, qDdeid) Dimensionless Total Material Balance Time, tDde,bar

  35. Conclusions 1. Developed a Real Space Analytical Solution for a Closed Rectangular Reservoir with One or More Wells • Can serve as analytical reservoir simulator. • Completely general formulation (constant rate, constant pressure, or variable-rate/pressure).

  36. Conclusions 2. This Solution Provides a Mechanism for the Decline Type Curve Analysis in a Multiwell Reservoir System • Conserves volume of the entire system. • Rigorous and accurate approach for estima-ting original oil/gas-in-place in the overall reservoir system and formation permeability in the local reservoir system. • Can use pressure-rate performance data for onlyone well to estimate original oil/gas-in-place. • Can be used for well performance monitoring. • The key for the decline type curve analysis in a multiwell system is to use total material balance time.

  37. Conclusions 3. We Have Successfully Demonstrated the Application of the New Method to Analyze Production Data From Arun Gas Field

  38. Recommendations for Extensions of This Work To extend this work, we recommend: • Including various reservoir outer boundary conditions other than the closed (no-flow) outer boundary. • Development and application of a method-ology to estimate the near-well skin factor.

  39. Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs Taufan Marhaendrajana Ph.D. Candidate Texas A&M University SPE International Paper Contest 5 October 1999

  40. Heterogeneous Reservoir Example Issues: Effect of a randomly heterogeneous medium? Accuracy of results?  In-place volume kh-product Uniqueness/meaning of the analysis?

  41. Well [1,1] Well [1,2] Well [1,3] Well [2,2] Well [2,3] Well [2,1] Bottom Hole Flowing Pressure, psi Well [3,3] Well [3,1] Well [3,2] Time, Days

  42. Well [1,1] Well [1,2] Well [1,3] Well [2,2] Well [2,3] Well [2,1] Oil Rate, STB/D Well [3,3] Well [3,1] Well [3,2] Time, Days

  43. All Curves Converge to a Single Material Balance Trend Material Balance Trend q/Dp, STB/D/psi Decreasing Permeability tbar,e = Np,field/q, Days

  44. 12 7 4 7 4 12 28 18 80 48 800 160 1x104 80 48 28 18 12 7 4 160 800 Heterogeneous Reservoir Example Dimensionless Rate Functions (qDde, qDdei, qDdeid) Dimensionless Total Material Balance Time, tDde

  45. Calculated Results(Randomly Heterogeneous Reservoir) k (md) OOIP (MMSTB) Well [1,1] 4.04 4,278 4,278 [1,2] 3.27 [1,3] 4,278 4.44 4,278 [2,1] 4.30 4,278 [2,2] 2.52 4,278 [2,3] 3.38 4,278 [3,1] 3.93 4,278 3.99 [3,2] 4,278 [3,3] 3.64

  46. Results: k,calc. (md) k,input (md) Well [1,1] 4.04 4.10 3.73 [3,3] 3.64 OOIP (Input) 4,278 MMSTB OOIP (Calc.) 4,278 MMSTB Observations: Individual well performance appears to be "homogeneous" Computed in-place volume is essentially exact Computes permeability represents harmonic average in well drainage area 3.73 4.10

  47. Well Pressure Solution (Continued) New Single-Well Solution: (Constant Rate) Characteristics: • Exact • Very fast (2-3 seconds/100 points)

  48. Well Pressure Solution

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