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Yohanes ASKABE Department of Petroleum Engineering Texas A&M University

Status Presentation College Station, TX (USA) — 12 August 2012. Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations — Montney Shale Case Histories.

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Yohanes ASKABE Department of Petroleum Engineering Texas A&M University

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  1. Status Presentation College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations —Montney Shale Case Histories (Alt.) Rate-Decline Relations for Unconventional Reservoirs and Development of Parametric Correlations for Estimation of Reservoir Properties Yohanes ASKABE Department of Petroleum Engineering Texas A&M University College Station, TX 77843-3116 (USA) yohanes.askabe@pe.tamu.edu Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  2. Outline: Objectives Introduction Rate-Time Models: PLE Model Logistic Growth Model (LGM) Duong Model Models performance analysis Modified rate decline models A Parametric correlation study Methodology: Analysis of time-rate model parameters Correlation of time-rate model parameters with reservoir/well parameters Development of Parametric Correlations Conclusions and Recommendations Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  3. Objectives/ Problem Statement: Ilk et al., (2011) have demonstrated that rate-time parameters can be correlated with reservoir/well parameters using limited well data from unconventional reservoirs. Theoretical verification and analysis of large number of high quality field data is necessary to test and verify the parametric correlations that correlate reservoir/well parameters with time-rate model parameters. This study will provide the opportunity to investigate performance of modern time-rate models in matching and forecasting rate-time data from unconventional reservoirs. The models considered are: PLE Model Logistic Growth Model (LGM) Duong Model Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  4. Introduction Modern time-rate models (PLE) have been shown to provide accurate EUR estimates and forecast future production when bottomhole flowing pressure (pwf) is constant. Time-Rate model Constraints: Constant Bottomhole Pressure (pwf) Constant Completion Parameters (Well lateral length, xf....) Time-Rate model parameters can be correlated with reservoir/well parameters (k, kxf, EUR) A diagnostic Approach Diagnostic Plots Data Driven matching process 'qdb' type diagnostic plot—discussed below Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  5. Governing Relations: Time-Rate Definitions • Time-Rate Analysis: Base Definitions • Based on the "Loss Ratio" concept (Arps, 1945). • Loss Ratio: • Loss Ratio Derivative: • Approach • Continuous evaluation of D(t)and b(t)relations provide a diagnostic method for matching time-rate data. • Diagnostic relations are used to derive empirical models. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  6. Time-Rate Analysis: Power Law Exponential History: SPE 116731 (Ilk et al., 2008) Derived from data (D(t) and b(t)) Analogous to Stretched-Exponential, but derived independently Has a terminal term for boundary-dominated flow (D∞) Governing Relations: Rate-Time relation: PLE Loss Ratio relation: PLE Loss Ratio Derivative relation: Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  7. Time-Rate Analysis: Duong Model History: SPE 137748 (Duong, 2011) Based on extended linear/bilinear flow regime Derived from transient behavior of unconventional-fractured reservoirs Relation extracted from straight line behavior of q/Gp vs. Time (Log-Log) plot Governing Relations: Duong Rate-Time relation: Duong Loss Ratio relation: Duong Loss Ratio Derivative relation: Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  8. Time-Rate Analysis: Logistic Growth Model (LGM) History SPE 144790 (Clark et al., 2011) Adopted from population growth models Modified form of hyperbolic logistic growth models Governing Relations: LGM Cumulative and Rate-Time relation: LGM Loss Ratio relation: LGM Loss Ratio Derivative relation: Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  9. Theoretical Consideration: Time-rate analysis • Well 1: k = 2000 nD • PLE Model • Transient • Transitional and • boundary-dominated flow regimes. • LGM Model • Transient and • Transitional flow regimes. • Duong Model • Transient flow regimes. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  10. Theoretical Consideration: Time-rate analysis • Well 1: k = 2000 nD • PLE • Excellent time-rate data match. • Accurate estimate of EUR is possible. • LGM and Duong Models • Excellent match during Transient flow regimes. • Lack boundary conditions. • EUR is overestimated. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  11. Theoretical Consideration: Time-rate analysis • Well 2: k = 50 nD • PLE, LGM and Duong Models. • All models match transient flow-regimes very well. • In the absence of boundary-dominated flow, all models provide reliable EURestimate. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  12. Theoretical Consideration: Time-rate analysis • Well 2: k =50nD • In the absence of boundary-dominated flow, PLE, LGM and Duong Models can: • match transient flow regimes very well and • provide good estimate of EUR. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  13. Modified Time-Rate Relations Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  14. Modified Time-Rate Models: Duong Model – (MODEL 1) Modified Duong Model With boundary parameter, DDNG Boundary-dominated flow can be modeled. Derivation is based on loss-ratiodefinition. The modified form of loss-ratio relation is given by: It is derived by assuming constant loss-ratio during boundary-dominated flow regimes. New time-rate relation can be derived from the loss-ratio relation. It is given by: Cumulative production relation can not be derived. Numerical methods are necessary. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  15. (Cont.) Modified Time-Rate Models: Duong Model - (MODEL 1) Modified Duong Model The loss-ratio derivative is given by: Modified Duong Model Boundary-dominated flows can be modeled. EUR estimates are constrained. Exponential decline characterizes boundary-dominated flow. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  16. Modified Duong Model: 'qdb' type diagnostic plot. (MODEL 1) • Derived based on loss-ratio derivation of Duong Model. • Modified Duong Model • Boundary-dominated flows can be modeled. • EUR estimates are constrained. • Exponential decline characterizes boundary-dominated flow. Added Constant Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  17. Modified Time-Rate Models: Duong Model - (MODEL 2) Modified Duong Model With boundary parameter DDNG Boundary-dominated flow can be modeled. Based on q/GpVs. timediagnostic plot. New q/Gpmodel-relation: New time-rate relation: New Cumulative productionrelation: Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  18. Modified Time-Rate Models: Duong Model - (MODEL 2) Cont. (Model parameters) The loss-ratio relation is given by: The loss-ratio derivative is given by: Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  19. Modified Time-Rate Models: Duong Model – (MODEL 2) • q/Gp vs. Time — Diagnostic Plot • On log-log plot of q/Gpvs. time: • Transient flow can be characterized by a power-law relation, and • Boundary-dominated flow can be characterized by an exponential declinerelation. • q/Gpdata can be matched with the following relation: Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  20. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  21. Modified Time-Rate Models: Duong Model (Cont.) Duong Model Modified Duong Model - (Model-2) Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  22. Duong Model: Diagnostic Plot (Cont.)- Montney Shale Wells vs. time Diagnostic Plot • m – Duong parameter describesrock-types, stimulation practices and fracture properties. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  23. Modified Time-Rate Models: Duong Model - (MODEL 2) • Numerical Simulation Case, k=8µD. • Model shows excellent data match for all flow regimes. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  24. Modified Time-Rate Models: Models Comparison • Model Comparison • Duong Model • Model 1 and • Model 2 • Modified Duong Models provide a better match • EUR is constrained. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  25. Modified Time-Rate Models: Models Comparison Numerical Simulation Case (k = 8 µD) • Model Comparison • Duong Model • Model 1 and • Model 2 • Modified Duong Models provide excellent match to Transient, Transition and boundary-dominated flow regimes. • Duong Model can also match observed early time Skin and production constraints. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  26. Modified Time-Rate Models: Logistic Growth Model (MODEL 3) Modified Logistic Growth Model With boundary parameter DLGM Boundary-dominated flow can be modeled. Modified LGM time-raterelation: Assuming exponential decline during boundary dominated flow regimes. Modified LGM Loss Ratio relation: Modified LGM Loss Ratio derivative relation: Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  27. Modified Logistic Growth Model: MODEL 3-qdb' type diagnostic plot. • Modified Logistic Growth Model: • Boundary-dominated flows can be modeled accurately • EUR estimates are constrained. • Exponential decline characterizes boundary-dominated flow. • Prior knowledge of gas in place (K) is required. • Direct formulation of Gp is not possible. Numerical methods are necessary. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  28. Modified Logistic Growth Model: (MODEL 4) • Using Diagnostic plot of [K/Qg– 1] vs. t or tmb From LGM Model we have • The last relation suggests that a log-log plot of [K/Qgt – 1] versus time shows a power-law relation for transient flow regimes. • Now, we can suggest the following relation with modification for boundary dominated flow regimes. Where K = Initial Gas in Place. R = Remaining Gas Reserve at t∞. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  29. Modified Logistic Growth Model: (MODEL 4) • Now, we can derive the associated modified relations. R = Remaining Gas Reserve at t∞ • Cumulative Production [Gp(t)] relation can be derived for Model 4. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  30. Modified Logistic Growth Model: Diagnostic Plot Corrected K/Q-1 Relation (MODEL 4) • If K is known, we can estimate parameters a and n from the transient flow regime. • .DLGMcan be modified based on boundary behaviors. a= 161 n= 0.79 K = 20,219,576.75 Dlgm = 0.00029 R = 0.157 Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  31. Modified Logistic Growth Model: Comparison (MODEL and MODEL 4) • Modified LGM models can match transient and boundary-dominated flow regimes better than LGMmodel. • EUR is constrained. • MODEL 4 provides a better match. • Gp relation can be derived for MODEL 4. • Prior knowledge of gas in place (K) is required. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  32. Theoretical Consideration: Synthetic Case Examples • A horizontal well with multiple transverse fractures is modeled. • The model inputs are as follows: Horizontal well with multiple transverse fractures Transverse Fractures • Synthetic Examples • 14 Models with permeability (k) ranging from 0.25 µD - 5µD. • All other reservoir/well and fluid parameters are identical. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  33. Parameter Analysis: PLE Time-Rate Model • PLE model parameters are related to EUR estimatesfrom PDA Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  34. Parameter Analysis: PLE Time-Rate Model • PLE model parameters are related to permeability Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  35. Parameter Correlation: Permeability • A parametric correlation that relates reservoir permeability with rate-time model parameters can be produced. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  36. Parameter Correlation: EUR • A parametric correlation that relates EUR estimates with rate-time model parameters can be produced. • The parametric correlation may not be unique. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  37. Field Data Example: Permeability • Field data example: Montney Shale, (Brassey)Wells • Careful analysis of pressure/production data is necessary to accurately estimate reservoir/well parameters (k, EUR, xf). • Decline curve analysis is then carried out to estimate EUR. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  38. Field Data Example: EUR • Field data example: Montney Shale, (Brassey)Wells • EUR is normalized by initial BHP (Pi), and number of effective fractures. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  39. Conclusion: • It is possible to integrate time-rate model parameters with reservoir/well parameters using parametric correlations. • Parametric correlations solve the uncertainty regarding the number of unknown parameters in model based production data analysis. • Modern rate decline models are successful at modeling different flow regimes observed from unconventional reservoirs. In summary: • PLE Model • Transient, transition, and, boundary-dominated flow regimes are successfully modeled. • Logistic Growth Model (LGM) • Transient, and transition flow regimes are successfully modeled. • Duong Model • Only transient flow regimes are matched. • EUR is overestimated. • Doesn’t conform to ‘qdb’ type diagnostic plot. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  40. Extra Slides Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  41. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  42. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  43. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  44. Summary: Model Comparison Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  45. Modified Logistic Growth Model: Corrected K/Q-1 Relation • LGM K (Carrying capacity) is equivalent to Gas in Place volumetric estimate. • Gas in place estimate should be available to use this model • K/Q(t)-1 vs. tmbdiagnostic plot can be used. Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  46. PLE Duong LGM Modified Duong MODEL 1 Modified Duong MODEL 2 Modified LGM MODEL 1 Modified LGM MODEL 2 Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  47. PLE Duong LGM Modified Duong MODEL 1 Modified Duong MODEL 2 Modified LGM MODEL 1 Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  48. Modified Time-Rate Models: Duong Model - (MODEL 2) Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  49. Power Law Exponential (PLE) Model Loss Ratio Relation Basis for PLE Model Rate-Time Relation Loss-Ratio Derivative Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

  50. Duong Time-Rate Relation q/Gp vs. Production Time Log-Log Plot Basis for Duong Model Rate-Time Relation Cumulative-Time Relation Loss-Ratio Loss-Ratio Derivative Status Presentation — Yohanes ASKABE — Texas A&M University College Station, TX (USA) — 12 August 2012 Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories

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