1. Chapter 5 Well Testing (III)
Weibo Sui
Ph.D, Associate Professor
College of Petroleum Engineering, CUPB

2. Type Curve What are type curves?
Type curves are graphic plots of theoretical solutions to flow equations under specific initial and boundary conditions of the interpretation model representing a reservoir-well system.
Most common type curves are presented in dimensionless pressure (pD) versus dimensionless time (tD) .

3. Infinite reservoir, line source well (Transient)

4. Agarwal Type Curve
Agarwal et al. (1970)

5. Type Curve Matching
Log-log type curve analysis make use of the dimensionless variables. Since dimensionless pressure and time are linear functions of actual pressure and time, we can calculate kh and φh:

7. Gringarten Type Curve

8. Bourdet’s Derivative Plot (1983)
The derivative plot provides a simultaneous presentation of log ∆p vs. log ∆t and log dp/d(lnt) vs. log ∆t.
Pressure change log-log plot (Gringarten)
Pressure change derivative log-log plot

9. Bourdet’s Derivative Plot (1983)

10. Wellbore Storage Effect (WBS)
During WBS, the pressure change is a linear function of time since the beginning of the transient:
Which means the unit slope. For the pressure change derivative:

11. Infinite Acting Radial Flow (IARF)

12. Combined Gringarten and Bourdet Plot

13. The Pressure Derivative

14. Pressure Derivative

15. Flow Regimes
Wellbore Storage
Radial Flow
Spherical
Linear
Bilinear

16. Radial Flow Regimes for Vertical Wells
Top of zone
Bottom of zone
Partial Radial Flow
Pseudoradial Flow to Fracture
Hemiradial Flow to Well Near Sealing Boundary
Fracture
Fracture Boundary
Actual Well
Image Well
Sealing Boundary
Complete Radial Flow

17. Radial Flow Regimes for Horizontal Wells
Pseudoradial flow
Radial flow
Hemiradial flow

18. Spherical Flow Regimes
Spherical Flow to Partially Completed Zone
Hemispherical Flow to Partially Completed Zone

19. Linear Flow Regimes Fracture Linear Flow Linear Flow to Fracture
Fracture Boundary
Fracture
Linear Flow to Fracture
Bilinear Flow
Linear Flow to Horizontal Well
Linear Flow to Well in Elongated Reservoir

20. Flow Regime Identification
Radial
Pseudosteady state
Well bore storage
Linear
Bilinear
Spherical
FRID Tool

21. Flow Region Identification
Wellbore Storage (WBS) - Estimate Cs, wellbore storage coefficient (bbls/psi)
Middle time region (MTR) - calculate skin, k & p*
Late Time region (LTR) - boundaries, kh variations (pi or p* for depleted reservoir)
Radial
Pseudosteady state
Well bore storage
Linear
Bilinear
Spherical

22. Time Region Identification

23. Early and Middle Time Analysis

24. Drawdown Analysis C, k, s cartesian plot (C) semilog analysis (k, s)
log-log derivative (C, k, s)

25. Drawdown Analysis

26. Cartesian Drawdown Analysis – CDp Dt mC
Zoom

27. Semi-log Drawdown Analysis – s

28. Log-Log Drawdown Analysis – C
log Dp
(Dt2, Dp2)
(Dt1, Dp1)

29. Log-Log Drawdown Analysis – k, s

30. PBU Analysis (straight line methods)
C, k, s, p*
cartesian plot (C)
semilog analysis (k, s, p*)
- log-log derivative (C, k, s, p*)

31. PBU Analysis

32. Cartesian PBU Analysis – CDp Dt mC
Zoom
Zoom

33. Horner PBU Analysis – k, p*
Semilog (Horner) Analysis 10 1 2 3
4980.
4985.
4990.
4995.
(Tp + dT)/dT
P PSI
Horner slope, m p*

34. Horner PBU Analysis – s p* Horner slope, m Semilog (Horner) Analysis10 1 2 3
4980.
4985.
4990.
4995.
(Tp + dT)/dT
P PSI
Horner slope, m p*

35. Log-Log PBU Analysis – C, k, s

36. Log-Log PBU Analysis – C
log Dp
(Dt2, Dp2)
(Dt1, Dp1)

37. Log-Log PBU Analysis – k, s

38. Finite Conductivity Hydraulic Fracture

39. Finite Conductivity Hydraulic Fracture
Radial
Pseudosteady state
Well bore storage
Linear
Bilinear
Spherical
Bilinear Flow (1/4 slope)
Linear Flow (1/2 slope)
Finite Conductivity Hydraulic Fracture
Time, hrs
Dp, Dp’, psi

40. Late Time Analysis

41. Late-Time Analysis: Outer Boundary
Drawdown
Time, hrs
Dp, Dp’, psi

42. Closed Boundary – PSS Flow

43. Closed Boundary – PSS Flow
Drawdown
Time, hrs
Dp, Dp’, psi

44. Rectangular Drainage Area

45. Boundary Models – Single Sealing Fault
Characteristic flow regimes:
Radial flow
Hemi-radial flow

46. Boundary Models – Single Sealing Fault

47. Boundary Models – Single Sealing Fault

48. Semi-log Plot

49. Boundary Models – Single Sealing Fault

50. Boundary Models – Single Sealing Fault

51. Dimensionless Pressure Derivative Plot

52. Dimensionless Pressure Derivative Plot

53. Intersecting Fault
θ = 60⁰
A 60 deg. angle between the intersecting faults is equivalent to the active well plus 5 image wells for a total of 6 effective wells. The derivative level will rise to 6 times the level of the initial radial flow response.

54. Intersecting Fault
q = 30o

55. Time Region Analysis Early-time analysis Middle-time analysis
wellbore storage
skin factor
Middle-time analysis
reservoir model (IARF, hydraulic fractured, natural fractured reservoir)
reservoir properties (permeability etc.)
Late-time analysis
outer boundary

56. Well Testing Analysis Procedures
Data plots
prepare log-log plots of pressure change and pressure change derivative vs. elapsed time during the test.
prepare special plots of the data (semi-log plot etc.)
Qualitative type-curve analysis
identify the appropriate reservoir model
identify any characteristic flow regime that can be analyzed with special analysis techniques
Semi-log or specialized analysis
estimate formation properties
Quantitative type-curve analysis
confirm or complement specialized analysis results

58. Cutting-Edge Well Testing Technique
Reservoir and well model
Various boundaries
Constant pressure, closed system, faults, composite reservoir, leaky fault, incomplete boundary
Naturally fractured reservoir, multilayer reservoir
Hydraulic fractured well, partially penetration well, horizontal well
Multiphase flow

59. Cutting-Edge Well Testing Technique
Pressure-Transient-Analysis Software
Initialization
Test design
Loading/editing data
Diagnostic tools
Modeling capability
Model selection, parameter estimation, numerical model
Optimization
Report generation

60. Permanent Downhole Gauge

61. In-Class Exercise PTT Ch2, Problem 16 PTT Ch2, Problem 37
Please use log-log pressure change derivative plot and semi-log plot to solve problem 1 and 2. Beside determining the parameters required in the problem, please determine the early-time, middle-time and late-time flow regime.
PTT Ch2, Problem 16
PTT Ch2, Problem 37

62. In-Class Exercise
The following table gives measured data for a buildup test for a finite-acting well. Before shut-in for buildup, the well pressure was declining linearly at psi/hr. Use this information to determine the following parameters.
(1) Reservoir pore volume, Vp
(2) Permeability-thickness product, kh
Reservoir Parameters
qBo, RB/D
333.3
ct, psi-1
8×10-6
μ, cp 2
m*, psi/hr
-0.431

63. t
(hours) p
(psia) 1 15 2 16 3 17 4 18 5 19 6 20 7 21 8 22 9 23 10 24 11 25 12 26 13 27 14 28

64. In-Class Exercise
A well is opened to flow at 150 STB/day for 24 hours. The flow rate is then increased to 360 STB/day and lasted for another 24 hours. The well flow rate is then reduced to 310 STB/day for 16 hours. Calculate the pressure drop in a shut-in well 700 ft away from the well given: