1. Chapter 5 Pressure Transient Testing (I)
Weibo Sui
Associate Professor
College of Petroleum Engineering, CUPB

2. Scope of the Chapter What reservoir/well testing is
What can be learned from a reservoir test
How to analyze test data

3. Reservoir/Well Testing
Dynamic reservoir description based on measurement of:
- flow rate (sandface/wellbore)
- pressure (sandface/wellbore)
- (temperature, density)

4. Schematic Diagram of a Well Test
packer
water
separator
choke
oil
gas
pressure, temperature gauge
wireline
perforations
formation

5. Typical Job Sequence
Flow well at single or multiple rates for time, tp
Shut well in for pressure buildup for time, Dt
Measure surface flow rates of all flowing phases, and bottomhole p, T

6. Test Types Drawdown Test Buildup Test DST (Drill Stem Test)
difficult to maintain constant rate
analysis unreliable
no lost production
Buildup Test
rate known, q = 0
analysis more reliable
production lost
DST (Drill Stem Test)

7. Drawdown Test
(5500 psi)
(2000 STB/D, 24 hrs)

8. Pressure Buildup Test (5800 psi) (1000 STB/D, 24 hrs)
(shut in for 24 hrs)

9. Multi-rate Test
(2000 STB/D)
(1500 STB/D)
(2500 STB/D)
(1000 STB/D)

10. Drill Stem Test – Flow to Surfacep q 3 9
15 hr
Run in hole
Short flow,
cleanup
Short
buildup
Long flow
Final buildup
Pull out of hole
pmud pR
Time, hr

11. Well Test – Field Case

12. Well Test – Field Case

13. Objectives for Transient Testing
Production Engineers
Average reservoir pressure
Productivity index
Skin
Rate dependent skin
Skin components
Post treatment skin after perforating, gravel packing, acid injection, or hydraulic fracturing

14. Objectives for Transient Testing
Reservoir Engineers
Reservoir characterization
Test radius of investigation
Formation permeability (vertical, horizontal)
Barriers to flow (sealing or leaky)
Shale bed boundaries
Structural limits (fault, salt dome, pinch out)
Stratigraphic limits (flow units, unconformities)

15. Objectives for Transient Testing
Exploration well :
confirm the exploration hypothesis;
establish a first production forecast: nature and rate of produced fluids, initial pressure etc.
Appraisal well :
well and reservoir description can be refined (well productivity, reservoir permeability, reservoir boundaries etc.)
Development well :
(periodic tests)
adjust the reservoir description
evaluate skin factor and the need of a well treatment, such as workover, perforation strategy etc.
evaluate communication between wells (interference testing)
monitor the average reservoir pressure

16. Well Testing Analysis Techniques
Mathematical models
Conventional straight line analysis
Type curve analysis
pressure change type curve (semi-log plot)
pressure derivative type curve (log-log plot)
Commercial software

17. Mechanisms Governing Transient Testing
Diffusivity Equation (P, q, r, t)
Assumption
circular, homogeneous reservoir with uniform thickness
well located in the center of reservoir, and fully penetrated producing intervals guarantee radial flow
slightly compressible fluid

18. Diagram of the Reservoir and Well

19. Diffusivity Equation Derivation of the diffusivity equation
Solutions for the diffusivity equation
Limiting forms for solutions of the diffusivity equation

20. Derivation of the Diffusivity Equation
Continuity equation – mass conservation
Darcy’s Law – flow through porous media
Equation of state

21. Continuity Equation – Mass Conservation

22. Continuity Equation – Mass Conservation

23. Continuity Equation – Mass Conservation

24. Continuity Equation – Mass Conservation

25. Continuity Equation – Mass Conservation

26. Continuity Equation – Mass Conservation

27. Continuity Equation – Mass Conservation
Assumptions: velocity in vertical and angular directions are zero

28. Darcy’s Law – Flow Through Porous Media

29. Darcy’s Law – Flow Through Porous Media

30. Equation of State - Liquid

31. Equation of State - Liquid

32. Diffusivity Equation - Liquid

33. Diffusivity Equation Derivation of the diffusivity equation
Solutions for the diffusivity equation
Limiting forms for solutions of the diffusivity equation

34. Reservoir Fluid Flow Regime
Transient flow
Pseudo-steady-state flow
Steady-state flow

35. Transient Flow
Pressure wave has not reached the reservoir boundary, reservoir acts like infinite. dp/dt varies with r, t.

36. Pseudo-Steday-State Flow (PSS)
Pressure wave has reached the reservoir outer boundary, there is no flow across the outer boundary. dp/dt = const.

37. Steady-State Flow (SS)
Pressure wave has reached the reservoir outer boundary, the outer boundary pressure is constant, and the rate of fluid flow into the reservoir at the outer boundary is equal to the well production rate. dp/dt = 0.

38. Solution for the Diffusivity Equation
Constant terminal rate solution (inner boundary)
(Well testing analysis)
Outer boundary
Infinite reservoir (Transient flow)
Bounded cylindrical reservoir
no-flow outer boundary (PSS)
constant-pressure outer boundary (SS)
Well treatment
Line source well (rw → 0)
Cylindrical source well (rw ≠ 0)
Constant terminal pressure solution (inner boundary)
(Aquifer influx model)

39. Bounded cylindrical reservoir, constant-pressure outer boundary (SS)

40. Bounded cylindrical reservoir, constant-pressure outer boundary (SS)
(SI Unit)

41. Bounded cylindrical reservoir, no-flow outer boundary (PSS)

42. Bounded cylindrical reservoir, no-flow outer boundary (PSS)

43. Bounded cylindrical reservoir, no-flow outer boundary (PSS)
(SI Unit)

44. Infinite reservoir, line source well (Transient)

45. Infinite reservoir, line source well (Transient)

46. Infinite reservoir, line source well (Transient)

47. Solution Derivation Using the Boltzman Transform

48. Solution Derivation Using the Boltzman Transform

49. Solution Derivation Using the Boltzman Transform

50. Solution Derivation Using the Boltzman Transform

51. Infinite reservoir, line source well (Transient)

52. Applicability of line source solution

53. Diffusivity Equation Derivation of the diffusivity equation
Solutions for the diffusivity equation
Limiting forms for solutions of the diffusivity equation

54. Limiting Forms

55. Flow States – Transient
SI Units:
Field Units:
Write equation in alternative form
Limited form:
In ‘log10’ :

56. Flow States – Pseudo-Steady State (PSS)
SI Units:
Field Units:
(Field Unit)

57. Flow States – Steady State
SI Units:
Field Units:
(Field Unit)

58. Exercise Sketch the pressure profile as a function of ln r for
Steady state
Pseudo-steady state
Transient state