1. Norwegian University of Science and Technology Well Test Analysis, Application to Thermal Recovery Processes for Reservoir Characterization Candidate: Ashkan Jahanbani Supervisors: Tom Aage Jelmert & Jon Kleppe (NTNU) M. Pooladi-Darvish (University of Calgary, now with IHS)

2. Norwegian University of Science and Technology 2 Introduction to Thermal Well Testing Statement of the Problem Development of A New Mathematical Model for Well Test Analysis Outline

3. Norwegian University of Science and Technology Radial System Flow Regime V k, s

4. Norwegian University of Science and Technology 4 Thermal Recovery Processes Donaldson et al. (1985)

5. Norwegian University of Science and Technology Thermal Well Testing Thermal well test analysis (falloff tests) can be used to estimate swept volume, which is in turn used to calculate: Heat loss Heat efficiency

6. Norwegian University of Science and Technology 6 Direct versus Inverse Solutions Inputsystem+Output (?) Convolution (Direct solution) Deconvolution (Inverse solution) InputSystem (?)+Output

7. Norwegian University of Science and Technology Radial Composite Reservoir

8. Norwegian University of Science and Technology 8

9. 9 Statement of the Problem Sharp vertical front 2-region model with sharp changes of properties at the front No heat loss

10. Norwegian University of Science and Technology 10 Modifications considered in this work Tilted front(s) due to gravity effects. 3-region composite reservoir model with smooth variation of properties. Inclusion of steam condensation in the form of heat loss.

11. Norwegian University of Science and Technology 11 Conventional Model Region 1 Region 2 R1R1 R2R2 H h rwrw rere No Heat loss to overburden No Heat loss to underburden

12. Norwegian University of Science and Technology 12 Development of the New Model

13. Norwegian University of Science and Technology 13 1) Tilted Fronts

14. Norwegian University of Science and Technology 14 2) Smooth Property Variation

15. Norwegian University of Science and Technology 15 Mass In - Out = Gain Continuity EquationEquation of StateDarcy Equation 3) Heat Loss G: rate of condensation per unit volume.

16. Norwegian University of Science and Technology 16 PDE for Different Regions

17. Norwegian University of Science and Technology 17 Continuity of pressure Continuity of flux Constant rate injection 1)Infinite-acting reservoir 2)No-flow boundary 3)Constant pressure boundary Solution

18. Norwegian University of Science and Technology 18

19. Norwegian University of Science and Technology 19 Model Validation

20. Norwegian University of Science and Technology 20 2-region composite models 3-region composite models

21. Norwegian University of Science and Technology 21 Effect of Heat Loss

22. Norwegian University of Science and Technology 22 Effect of Size of Middle-region

23. Norwegian University of Science and Technology 23 Effect of Front Angle

24. Norwegian University of Science and Technology 24 Thanks for your attention