Usage of X-ray CT in Dual Porosity Simulation.

1. Usage of X-ray CT in Dual Porosity Simulation. Prasanna K Tellapaneni

2. Motivation Problem Definition Objectives Approach Validation Conclusions Presentation Outline

3. Primary Porosity Micro-Fractures/Fractures Secondary Porosity Vugs Dual Porosity Actual Grid Block Idealized Grid Block

4. Dual Porosity Motivation Shape Factor Shape factor is the bone of contention in dual porosity simulation.

5. There are 23 transfer functions present in the literature – Ries and Cil (1998) No experimental backing Motivation

6. Motivation • Other assumptions • Linear pressure gradient • “Pseudo-Steady State” assumption of matrix blocks • Rn = n(R1) • Four unknowns per grid block.

7. Problem Definition Imbibition laboratory experiments are excluded in dual porosity simulation

8. Modeling imbibition experiments to obtain unique transfer function. Development of a dual porosity simulator with the derived empirical transfer function and its validation. Objectives

9. Approach • Develop Dual Porosity Simulation Formulation • Model Imbibition Experiments • Derive Empirical Transfer Function • Validate with a Commercial Dual Porosity Simulator

10. Approach Dual Porosity Flow Equations Conventional Dual Porosity

11. Approach Combining Aronofsky (1958) and deSwaan (1978) Empirical Transfer Function

12. Data acquisition system Weight Balance Core Water Tank Approach Imbibition Experiments Garg et al Experiment

13. Oil recovered Oil bubble Glass funnel Core plug Brine Approach Governing Equation Assumptions  No gravity effect Only Pc as driving force Fluid and rock are incompressible   Spontaneous Imbibition Modeling in Single Porosity Simulation Spontaneous Imbibition Experiments Spontaneous Imbibition in Double Porosity Modeling

14. Approach Corey’s Correlation We need X-ray CT

15. X-Ray Detectors X-Ray Emitters Approach X-ray CT Imbibition Experiments

16. Approach X-ray CT Result Simulation Result 160s 120s 80s 80s 160s 120s 200s 320s 360s 320s 360s 200s

17. Krwo= 0.045 and N=8.5 Approach

18. Approach Curve Fitting Parameters Rinf = 1.0 lamda = 0.031

19. Approach Recalling the flow equations In order to solve this non-linear equations we use Newton-Raphson’s method.

20. Discretizing using finite difference Approach Writing oil-phase equation Expanding

21. Approach The equations can be written as Writing the Taylor Series Expansion Newton Raphson’s Solution

22. Kazemi et al (SPE 5719) 2 – D Kazemi Grid (Extension of SPE 5719) Validation • Comparison with Sub Domain Method

23. Validation Kazemi et al (SPE 5719)

24. Validation Kazemi et al 2-D grid

25. Validation Pressure profile along a line parallel to X axis

26. Validation Sub Domain Method Matrix Matrix Matrix Fracture Fracture Fracture Dual Porosity Sub Domain Method

27. Validation

28. Stability Material Balance Limitations

29. Empirical transfer functions are proposed for dual porosity simulation X-ray CT is used for modeling imbibition experiments Dual porosity simulator is developed and validated with test cases. Recap

30. Conclusions Conventional Dual Porosity This Study • Two unknowns per grid block. • Four unknowns per grid block. • Honors experiments – derived from experiments. • No experimental backing – based on Darcy’s Law • Non-Standard Formulation. • Standard Formulation

31. Conclusions Conventional Dual Porosity This Study • Fewer “Best Guess” values • Too many “Best Guess” values • Linear pressure gradient. • Pressure difference is not used. • Rn = nR1 • Rn = sum(Ri) • Psuedo-steady state assumption • Even transient state is modeled.

32. Standardized formulation of dual porosity simulation Reduction in simulation time and computation efficiency Better reservoir management by accurate fluid flow simulation Value to the industry

33. Dr. Schechter, Texas A&M University Dr. Erwin Putra, Texas A&M University Department of Energy Acknowledgement

34. Usage of X-ray CT in Dual Porosity Simulation. Prasanna K Tellapaneni